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See GWIC_Science_Book_Cover_wdate

.

.

Out of the cosmic rife, I just picked me a star
another came along, from not so far
Thought it would be a real good bet
The best is yet to come

The best is yet to come and may be, it’ll be fine
You think you’ve seen the sun
But you ain’t seen two rattle and shine

A wait till the 3rd-gen’s underway
Wait till our feisty stars have met
And wait till you see that everyday
You ain’t seen nothing yet.
— Sanjay Reddy with apologies to Frank Sinatra

Front Cover: Artist’s impression of a black hole-neutron star merger, Carl
Knoz, OzGrav

SCIENCE BOOK SUBCOMMITTEE
Vicky Kalogera, Northwestern University, USA (Co-chair)
B.S. Sathyaprakash, Penn State USA and Cardiff University, UK (Co-chair)
Matthew Bailes, Swinburne, Australia
Marie-Anne Bizouard, CNRS & Observatoire de la Cote d’Azur, France
Alessandra Buonanno, AEI, Potsdam, Germany and University of Maryland, USA
Adam Burrows, Princeton, USA
Monica Colpi, INFN, Italy
Matt Evans, MIT, USA
Stephen Fairhurst, Cardiff University, UK
Stefan Hild, Maastricht University, Netherlands
Mansi M. Kasliwal, Caltech, USA
Luis Lehner, Perimeter Institute, Canada
Ilya Mandel, University of Birmingham, UK
Vuk Mandic, University of Minnesota, USA
Samaya Nissanke, University of Amsterdam, Netherlands
Maria Alessandra Papa, AEI, Hannover, Germany
Sanjay Reddy, University of Washington, USA
Stephan Rosswog, Oskar Klein Centre, Sweden
Chris Van Den Broeck, Nikhef, Netherlands

STEERING COMMITTEE
Michele Punturo, INFN Perugia, Italy (Co-chair)
David Reitze, Caltech, USA (Co-chair)
Peter Couvares, Caltech, USA
Stavros Katsanevas, European Gravitational Observatory
Takaaki Kajita, University of Tokyo, Japan
Vicky Kalogera, Northwestern University, USA
Harald Lueck, AEI, Hannover, Germany
David McClelland, Australian National University, Australia
Sheila Rowan, University of Glasgow, UK
Gary Sanders, Caltech, USA
B.S. Sathyaprakash, Penn State University, USA and Cardiff University, UK
David Shoemaker, MIT, USA (Secretary)
Jo van den Brand, Nikhef, Netherlands
Gravitational Wave International Committee

This document was produced by the GWIC 3G Committee, the GWIC 3G Science Case
Team and the International 3G Science Team Consortium

Final release, April 2021

Additional Authors

P. Ajith, International Centre for Theoretical Sciences, India
Shreya Anand, Caltech, USA
Igor Andreoni, Caltech, USA
K.G. Arun, Chennai Mathematical Institute, India
Enrico Barausse, SISSA, Italy
Masha Baryakhtar, New York University, USA and University of Washington, USA
Enis Belgacem, Utrecht University, The Netherlands
Christopher P.L. Berry, Northwestern University, USA
Daniele Bertacca, Università degli Studi di Padova, Italy and INFN Sezione di
Padova, Italy
Richard Brito, Sapienza University of Rome, Italy
Chiara Caprini, Université Paris-Diderot, France
Katerina Chatziioannou, Caltech, USA
Michael Coughlin, University of Minnesota, USA
Giulia Cusin, University of Geneva, Switzerland
Tim Dietrich, University of Potsdam, Germany
Yves Dirian, University of Geneva and University of Zuerich, Switzerland
William E. East, Perimeter Institute, Canada
Xilong Fan, Wuhan University and Hubei University of Education, China
Daniel Figueroa, École Polytechnique Fédérale de Lausanne, Switzerland
Stefano Foffa, University of Geneva, Switzerland
Archisman Ghosh, Ghent University, Belgium
Evan Hall, MIT, USA
Jan Harms, Gran Sasso Science Institute, Italy
Ian Harry, Max Planck Institute for Gravitational Physics, Potsdam, Germany
and University of Portsmouth, UK
Tanja Hinderer, Utrecht University, The Netherlands
Thomas Janka, Max Planck Institute for Astrophysics, Germany
Stephen Justham, University of the Chinese Academy of Sciences, China and
University of Amsterdam, The Netherlands
Dan Kasen, University of California Berkeley, USA
Kei Kotake, Fukuoka University, Japan
Geoffrey Lovelace, California State University Fullerton, USA
Michele Maggiore, University of Geneva, Switzerland
Alberto Mangiagli, Astroparticule et Cosmologie, France
Michela Mapelli, University of Padova and INFN Padova, Italy
Andrea Maselli, Gran Sasso Science Institute, Italy
Andrew Matas, Max Planck Institute for Gravitational Physics, Potsdam, Germany
Jess McIver, Caltech, USA and the University of British Columbia, Canada
Bronson Messer, ORNL and University of Tennessee, USA
Tony Mezzacappa, ORNL and University of Tennessee, USA
Cameron Mills, Cardiff University, UK
Bernhard Mueller, Monash University, Australia
Ewald Müller, Max Planck Institute for Astrophysics, Germany
Michael Pürrer, Max Planck Institute for Gravitational Physics, Potsdam,
Germany
Paolo Pani, Sapienza University of Rome, Italy
Geraint Pratten, University of Balearic Islands, Spain and University of
Birmingham, UK
Tania Regimbau, Université Grenoble Alpes, France
Mairi Sakellariadou, Kings College London, United Kingdom
Raffaella Schneider, INFN Roma, Italy
Alberto Sesana, Università di Milano-Bicocca, Italy
Lijing Shao, Kavli Institute for Astronomy and Astrophysics, Peking
University, China
P. Thomas Sotiriou, The University of Nottingham, UK
Nicola Tamanini, Laboratoire des 2 infinis - Toulouse, France
Thomas Tauris, Aarhus University, Greece
Eric Thrane, Monash University, Australia
Rosa Valiante, INAF Roma, Italy
Maarten van de Meent, Max Planck Institute for Gravitational Physics, Potsdam,
Germany
Vijay Varma, Caltech, USA
Justin Vines, Max Planck Institute for Gravitational Physics, Potsdam, Germany
Salvatore Vitale, MIT, USA
Huan Yang, Perimeter Institute and University of Guelph, Canada
Nicolas Yunes, University of Illinois Urbana-Champaign, USA
Miguel Zumalacarregui, Max Planck Institute for Gravitational Physics,
Potsdam, Germany and University of California Berkeley, USA

###### Contents

  1. Executive Summary
  2. 1 Introduction
    1. 1.1 Prologue
    2. 1.2 Extreme Matter, Extreme Environments.
    3. 1.3 Observing Stellar-mass Black Holes Throughout the Universe.
    4. 1.4 Cosmology and Early History of the Universe.
    5. 1.5 Extreme Gravity and Fundamental Physics.
    6. 1.6 Sources at the Frontier of Observations
    7. 1.7 Summary
  3. 2 Extreme Matter, Extreme Environments
    1. 2.1 Nature of Matter at Highest Densities
    2. 2.2 Nucleosynthesis in Neutron Star Binary Mergers
    3. 2.3 Formation, Demographics and Merger Sites of Compact Binary Mergers
    4. 2.4 Jet Physics in Neutron Star Binary Mergers
    5. 2.5 Outlook for Extreme Matter and Extreme Environments
  4. 3 Observing Stellar-mass Black Holes Throughout the Universe
    1. 3.1 A survey of BHs throughout cosmic time
    2. 3.2 Expanding the BH mass spectrum
    3. 3.3 High-precision measurements of binary properties
    4. 3.4 Multiband gravitational-wave observations
    5. 3.5 Outlook for black hole gravitational-wave astronomy
  5. 4 Cosmology and the Early History of the Universe
    1. 4.1 Standard Siren Cosmology
    2. 4.2 Early History of the Universe
    3. 4.3 Astrophysical Binary Foregrounds and Large Scale Structure
    4. 4.4 Outlook for gravitational-wave cosmology and the early Universe
  6. 5 Extreme Gravity and Fundamental Physics
    1. 5.1 Nature of Gravity.
    2. 5.2 Nature of Compact Objects.
    3. 5.3 Nature of Dark Matter.
    4. 5.4 Outlook on Exploring Extreme Gravity and Fundamental Physics
  7. 6 Sources at the Frontier of Observations
    1. 6.1 Core-Collapse Supernovae
    2. 6.2 Sources of Continuous GWs
    3. 6.3 GW Bursts Associated with NS Flares and Glitches
    4. 6.4 Outlook for GW sources at the frontier of observations
  8. Acronyms & abbreviations

## Executive Summary

Within the last century, we have discovered incredible new truths about the
Universe using telescopes and particle detectors. We now know it is expanding
and composed mostly of dark matter and dark energy that we do not yet
understand and neutrinos and ultra high-energy particles, whose origin remains
a puzzle. We have learned that it harbors astounding entities such as black
holes, regions of spacetime so strongly warped that nothing, even light, that
falls inside can ever escape. We have learned that it is gravity that shapes
the structure of the Universe, from enormous cosmic fibers of matter to
galaxies and solar systems, to planets, stars, and black holes. Gravity drives
the most extreme phenomena in the Universe, including incredibly violent
collisions of black holes that in nearly an instant release millions of times
the energy that our Sun will emit in its entire lifetime.

Gravity encodes information about distant cosmic phenomena in a messenger
entirely different from light and particles: gravitational waves, tiny ripples
in the fabric of spacetime emitted by accelerating mass. Unlike light and
particles, gravitational waves interact weakly with matter, so they travel
vast distances almost entirely unobscured by dust, the Milky Way, or the Earth
itself. They offer a crystal clear signature of highly energetic phenomena
otherwise hidden from us.

Gravitational waves from a binary black hole merger observed by Advanced LIGO
in 2015 gave us our first glimpse of hugely energetic events that are
undetectable with light. Detectors on Earth capture gravitational waves
emitted by black holes orbiting so quickly that they approach the speed of
light before colliding. The first detections also revealed a population of
black holes with masses never before observed and charted the existence of
black holes formed by collapsed stars farther from Earth than ever before.

Black Holes: Where the Cosmos meets the Quantum Realm A new generation of
detectors will allow us to push Einstein’s general theory of relativity to the
limit and to test alternative theories that aim to resolve the fundamental
contradictions between quantum physics, which describes the Universe at very
small sizes, and general relativity, which describes the Universe at very
large sizes. Although the two are incompatible with each other, no experiment
yet has discovered new physics outside of either theory. Black holes provide a
laboratory that smashes these theories together; squeezing enormous masses
into infinitesimally small volumes. By sensing black hole collisions with high
fidelity, new detectors would allow us to test completely new regimes of
highly warped spacetime that could provide critical insight into this current
paradox in physics. The precision of next generation detectors would also
allow us to search for a differing gravitational-wave signature of new types
of exotic compact objects unlike black holes as we currently understand them.

A network of next-generation gravitational-wave detectors will survey the
extreme Universe with an unprecedented reach into deep space, beyond the
cosmic dawn when the first stars began to shine.

They will sample stellar-mass black hole mergers across the visible Universe,
observing these systems over the entire history of the cosmos, and chronicle
the evolution of black holes from the earliest mergers and inform if they grow
from collapsed stars to supermassive black holes at the center of galaxies,
billions of times as massive as our Sun.

The 2017 observation of the merger of two neutron stars by LIGO and Virgo and
its aftermath with the full spectrum of electromagnetic (EM) radiation was a
spectacular first success of multimessenger astronomy with gravitational waves
that reaffirmed theoretical models of the brightest EM events. Next-generation
ground-based gravitational-wave detectors will have the unique capability to
observe the violent mergers of neutron stars and their aftermath at far
greater distances and with the much higher precision required to address
outstanding problems in the physics of dense objects. Neutron stars are only
the size of a city yet contain more mass than the sun. They are the densest
material objects in the Universe, where intense gravity completely obliterates
the atomic structure of matter familiar to us. Even quarks—the tiniest
constituents that remain confined inside neutrons and protons in ordinary
matter—are likely to be liberated in the neutron star core.

Next generation detectors will allow us to observe neutron star mergers and
peek directly into their cores as they tear each other apart by tidal forces
before smashing together. These observations are critical to infer new
knowledge and understanding about nuclear physics and the states of matter
containing quarks. With next-generation multimessenger astrophysics enabled by
new detectors, we will learn how much of the Universe’s gold and platinum was
produced by neutron star collisions.

Observing the Universe on all Scales The diagram shows physical phenomena on
different scales explored by gravitational-wave observations. Starting from
the scale of the Universe, almost 100 billion light years, represented by the
cosmic microwave background at the top, the diagram progressively shows scales
that are smaller than the previous ones by the factor shown on the left. On
scales about 1000 times smaller are giant galaxy clusters 30 million light
years across. Another factor 10 million smaller is the size of a supernova
remnant of 10 light years. A trillion times smaller still is the merger
environment of binary neutron stars about 100 km across. The core of a neutron
star, about 1 km, is a trillion times smaller and contains matter at densities
similar to that of atomic nuclei. On scales ten thousand smaller still
gravitational waves could probe the nature of dark matter.

Furthermore, gravitational waves from binary black holes and neutron stars are
standard sirens—the distance to the source is encoded in the observed
gravitational waves. Thus, merging binaries provide a new precision tool for
observational cosmology that will help us gain new insight into how the
Universe is expanding and evolving and if dark energy is just a cosmological
constant or if there is missing new physics associated with the late-time
accelerated expansion of the Universe.

We will also achieve unprecedented insight into cosmic explosion mysteries.
Multimessenger astronomy with next generation detectors will allow us to
better investigate why core-collapse supernovae explode to seed the formation
of new stars and whether starquakes cause mysterious bursts of radio emission.
And as with any completely new method of observation, there is also the
possibility that next generation detectors will reveal completely new dark
phenomena, unseen with light, that we have not yet conceived of.

Today’s gravitational-wave detectors are barely sensitive enough to detect the
loudest gravitational waves in the Universe, like a simple radio able to pick
up only the loudest signals. Next-generation network detector designs leverage
cutting-edge technology to surpass current ground-based detectors, making
their ability to measure passing gravitational waves more than ten times
better than the current instruments.

Artists Conception of Einstein Telescope (left) and Cosmic Explorer (right)

Artists conception of the Einstein Telescope (left panel) and Cosmic Explorer
(right panel) observatories. ET is conceived to be six, V-shaped, underground
interferometers, formed out of 10 km sides of an equilateral triangle, while
Cosmic Explorer is conceived to be an L-shaped, overground interferometer,
with 40 km arms.

More powerful detectors will let us listen to the gravitational-wave universe
with unprecedented fidelity, fully revealing the rich physics encoded in the
waves but currently hidden by observational uncertainty. Einstein Telescope
(ET) is a European design featuring six V-shaped interferometers in a
triangular topology with 10 km interferometer arms and Cosmic Explorer (CE) is
a U.S. design for one or two interferometers with 40 km L-shaped
interferometer arms. ET and CE are expected to detect hundreds of thousands of
mergers, as well as tens of thousands of multimessenger sources that would
also likely emit EM radiation and particles that telescopes and neutrino and
cosmic ray detectors can observe. A network of three detectors distributed
around the globe will triangulate the gravitational wave signal’s location in
the sky, critical information that will guide telescopes on Earth and in space
in searches for related EM emission.

21st century astronomy will be further revolutionized by the launch of the
space-based LISA gravitational-wave observatory, expected in 2034. LISA will
sense gravitational waves emitted by more massive systems than ground-based
detectors, detecting the signature of orbiting black hole systems up to years
before ground-based detectors observe them collide. Combining space-based and
ground-based observations will allow us to catalog a much broader expanse of
the extreme gravitational Universe than ever before.

Gravitational waves have already given us a first glimpse of the dark, hidden,
violent Universe. A global next-generation gravitational wave observatory will
propel the field of astrophysics and all foundational science research
forward. Observing light, neutrinos and cosmic rays in concert with next-
generation gravitational wave detectors will launch enormous advances beyond
the current limits of human knowledge, from the quantum realm to the largest
cosmological structures in the known Universe.

##  Chapter 1 Introduction

###  1.1 Prologue

On 14 Sep 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO)
transformed the way we explore the universe. With LIGO, we were able to sense,
for the first time, the gravitational-wave (GW) sky. The signal came from the
merger of two black holes at a distance of 1.3 billion light years. This was
also when binary black holes were discovered and, for the first time, their
merger was observed. The masses of the companions, 29 and 36 solar masses,
were unexpectedly heavy and the merger converted some 3 solar masses into
energy in a mere 200 ms. Since that first discovery, many more black hole
mergers have been found by LIGO and the European Virgo, some with masses as
small as 2.6 solar masses, heaviest neutron star or lightest black hole, and
others as large as 85 solar masses, so large that they could not have formed
from the evolution of massive stars. In most cases the component black holes
seem to be non-spinning, contrary to what X-ray observations indicate.

Two years later, on 17 Aug 2017, a new era in multimessenger astronomy began
with the observation by LIGO and Virgo of the merger of two neutron stars,
followed by the detection, 1.7 s later, of a gamma-ray burst from the same
source by the Fermi gamma-ray space telescope and INTEGRAL. These observations
could together localize the event well enough that its host galaxy was quickly
found by optical telescopes. The merger produced spectacular fireworks that
were captured by telescopes across the entire electromagnetic (EM) spectrum
from radio to infrared and optical to X-rays. This treasure trove of data gave
us answers to decades old puzzles in fundamental physics and astronomy:
verified that GWs travel essentially at the speed of light, confirmed that
binary neutron star mergers are progenitors of short gamma ray bursts and
prolific sites for the formation of heavy elements, measured the Hubble
constant in a completely new way using GWs for the source’s distance and EM
observations for its redshift and constrained neutron-star radii to be between
9.5 and 13 km by measuring the tidal deformation of neutron stars.

The LIGO and Virgo detectors are yet to achieve their design sensitivities.
They will be augmented with new facilities, the Japanese KAGRA and LIGO-India.
Yet, based on the modest glimpses of the sources discovered to date, we know
that the full exploration of the GW sky will require a new generation of
detectors of a size that demands new facilities. With the aid of such
detectors we will be able to observe sources at the edge of the Universe,
unveil the properties of matter at the highest densities in the cosmos,
provide a new precision tool for observational cosmology and explore the
nature of dynamical spacetimes. A detector network with a leap in sensitivity
will resolve signals with far greater precision and fidelity that will pave
the way for serendipitous discoveries, observing novel phenomena and
unearthing new physics.

Beyond Advanced Detectors: During 2008-2011 the design study of a third
generation (3G) GW observatory in Europe, Einstein Telescope (ET), developed
the concept of a triangular interferometer, 10 km on a side, housing six
V-shaped interferometers whose combined sensitivity is a factor $\sim 20$
better than Advanced Virgo and pushing the low-frequency sensitivity down from
10 Hz to 3 Hz. A similar effort is currently underway in the US to study the
science case for and technical design of a 40 km arm length interferometer
called Cosmic Explorer (CE), with sensitivity similar to ET (see Figure 1.1,
left plot). For the current study we assume that _the 3G network_ consists of
one ET in Europe and one CE each in the US and Australia. A network of at
least three sites is required to accurately localize sources in the sky and
infer their distances. ET alone could measure the wave’s polarization but
cannot resolve all the parameter degeneracies to determine the sky position
even when the signals last for days.

The science potential of the 3G network is immediately apparent from the
dramatic improvement in strain sensitivity that CE and ET are able to deliver
(Figure 1.1, right panel). The network makes a leap of 1–2 orders of magnitude
in the redshift reach for binary coalescences compared to Advanced LIGO and
Virgo. The network will survey a large redshift range for merging binary black
holes and provide a massive catalog of detections to constrain their
population and origins. The network will explore a wide parameter space of
quantum chromodynamics and study high density matter in a region complementary
to heavy ion physics experiments. The Box below summarizes the science
potential of a 3G observatory, elucidated in the next several paragraphs.

Science Targets for the Next Generation of Gravitational Wave Detectors GW
astronomy provides a complementary window to EM, neutrino and particle
astronomy that could reveal hitherto unseen world. A new generation of
detectors will: • determine the properties of dense matter, discover phase
transitions, and the emergence of quarks • reveal merging black holes across
the cosmos and _search_ for seeds of supermassive black holes • investigate
the particle physics of the primeval Universe and probe its dark sectors •
explore new physics in gravity and in the fundamental properties of compact
objects • understand physical processes that underlie the most powerful
astrophysical phenomena

Sensitivity of ET and CE compared to Advanced LIGO & the Reach for 3G
Observatories

Figure 1.1: GW strain noise for current and future detectors (left) and
astrophysical reach for equal-mass, nonspinning binaries distributed
isotropically in sky and inclination (right).

###  1.2 Extreme Matter, Extreme Environments.

Neutron stars are the densest objects in the cosmos and sites of stupendously
strong magnetic fields, up to billions of tesla. Six decades after their
discovery, we still lack a clear understanding of the equation of state of
their deep cores and the origin of their strong magnetic fields. Neutron stars
in binaries are subject to the tidal fields of their companions although the
tides raised are extremely small. The extent of tidal deformation depends on
the internal structure of neutron stars and the net effect is to accelerate
the rate of inspiral allowing to read-off their internal structure from the
observed phase evolution of the signal. The merger remnant could be a rapidly
rotating, short-lived, hypermassive neutron star that eventually collapses to
a black hole. GWs from the merger will lead to tight measurements of NS radii
and hence reveal the equation of state of both cold and hot, supranuclear
matter and the deconfinement phase transition of quarks and gluons.

The origin of heavy elements in the Universe has been a long-standing problem.
EM observation of GW170817 provided irrefutable evidence that binary neutron
star mergers are prolific sites for the production of lanthanides and other
heavy elements. The 3G network will facilitate EM follow-up of thousands of
mergers, a number that is required to confirm if solar and stellar abundance
of heavy elements can be explained by mergers alone or if other production
channels, such as supernovae, are necessary.

GW170817 resolved that binary neutron star mergers are progenitors of short
gamma-ray bursts. Nevertheless key questions about central engines that
produce gamma rays still remain. For example, we do not have a clear picture
of the jet properties nor how those properties depend on the progenitor
characteristics. EM follow-up facilitated by the 3G network will allow a
better understanding of the physics of gamma-ray jets, the opening angle of
the jet and its distribution; GWs could tell us the nature of the merger
remnant and if the central engine is a transient hypermassive neutron star or
a promptly collapsed black hole.

3G observatories will detect binary neutron star mergers from epochs far
before the peak of star formation activity. Millions of mergers are expected
to be detected by the 3G network. The properties of the detected sources and
the environments in which they occur will provide key data to test
astrophysical models of the formation and evolution of double neutron star and
black hole-neutron star binaries, while also informing the history of star
formation activity up to redshifts of 5–8.

###  1.3 Observing Stellar-mass Black Holes Throughout the Universe.

The 3G network will have nearly all-sky sensitivity, detecting stellar-mass
black hole binaries of $\sim 10$–100 solar mass from epochs before the first
stars formed at redshifts $z\sim 30$ (Figures 1.1 and 1.3). Consequently, the
3G network could reveal a population of primordial black holes in this mass
range formed by quantum processes in the early Universe, in addition to
compiling a census of black holes over a range of masses throughout the
cosmos.

The merger rate of binary black holes observed so far imply that the 3G
network will detect hundreds of thousands of mergers each year. This large
population will help us study the merger rate as a function of redshift up to
the beginning of the epoch of reionization. It will also help us explore how
these rates are correlated with metallicity and galaxy evolution.

Visibility of Black Hole Binaries in 3G Figure 1.2: Signal-to-noise ratio
contours as a function of binary’s total mass and its redshift for equal mass
binaries averaged over sky position and orientation in the 3G network.

Until 2015, it was widely believed that irrespective of how massive a
progenitor star was the black hole that resulted from it would be lighter than
about 20 solar masses. LIGO and Virgo have detected many black holes with
masses in excess of that number. Indeed, GW190521 revealed a black hole of 85
solar masses that, theory says, cannot form from massive stars. Understanding
how such black holes form and if they grow through repetitive mergers is an
outstanding question in astrophysics. There are a number of competing models.
Black holes that form in isolation in globular clusters could sink into the
dense cluster cores where they dynamically interact with other holes to form
coalescing binaries. Binaries of massive stars formed in active star formation
sites could directly evolve into binary black holes that merge within the
Hubble time. If primordial black holes significantly contribute to dark matter
then they could occasionally form merging binaries in galactic halos. The 3G
network will pin down the masses, spins and demographics of black holes,
determine principal formation channels and resolve fundamental questions about
their origin.

###  1.4 Cosmology and Early History of the Universe.

GWs from the inspiral and merger of compact binaries can be used to infer the
luminosity distance to their sources without the need to calibrate them with
standard candles. This is because the orbital dynamics of binary black holes
and neutron stars is largely determined by Einstein’s theory of gravity. A
handful of parameters, e.g. masses and spins of the companion stars, precisely
control the pattern of the emitted GWs. The amplitude of that pattern is fixed
by the distance to the source, sky position and orientation of the source
relative to a detector, which can be inferred with a network of three or more
non-collocated detectors. This contrasts with the dynamics of other
astrophysical systems, such as supernovae, that require detailed modelling of
their composition and environment, making it extremely hard to predict the
emitted GW signal with any precision. Consequently, with a population of
compact binary mergers observed with 3G detectors, and their redshifts
obtained by follow-up EM observations, it will be possible to accurately
measure cosmological parameters such as the Hubble parameter, dark matter and
dark energy densities and the equation-of-state of dark energy, giving a
completely independent and complementary measurement of the dynamics of the
Universe.

The cosmological population of point sources create a stochastic GW
background. Indeed, with advanced interferometers we could detect the
background created by binary black holes and neutron stars throughout the
Universe and can do so by cross correlating data from two or more detectors.
Such backgrounds would reveal the history of the formation and evolution of
these sources and the underlying stellar population. On the contrary, 3G
detectors will identify most compact binary mergers in the Universe, giving us
a treasure trove of data to study the large-scale distribution of galaxies and
their clusters.

Stochastic GWs could also be produced in the early Universe. As the Universe
cools from its primeval hot and dense state it undergoes several phase
transitions that are expected to generate GW backgrounds. Detection of such
backgrounds would dramatically transform our state of knowledge of the
underlying particle theory at energy scales that will never be accessible to
terrestrial accelerators. Defects, such as cosmic strings, associated with
symmetry breaking phase transitions, could also produce stochastic and
deterministic signals. The landscape of primordial sources, while uncertain,
is a high-risk, high-reward endeavor to pursue in the era of 3G detectors.

###  1.5 Extreme Gravity and Fundamental Physics.

GWs emanate from regions of strong gravity and large curvature, carrying
uncorrupted information from their sources. Imprint in the signal is the
nature of the gravitational field, characteristics of the sources and the
physical environment in which they reside. Their observation in 3G detectors
can put general relativity to the most stringent tests, help explore
violations of the theory in strong fields such as the dynamics of black hole
horizons, and discover properties of dark matter.

The 3G network offers numerous opportunities to discover failure of general
relativity, e.g. in the form of new particles and fields that violate the
strong equivalence principle. It is also possible to detect Lorentz invariance
violations or variation in Newton’s constant, both imprint in the propagation
of GWs. One might also see the signature of quantum gravity in the form of
parity violation seen in the nature of the GW polarization or in the
birefringence of the waves propagating over great distances. Ultra-light
Bosonic fields proposed in certain extensions of the Standard Model could be
detected via their effect on the orbital dynamics of black hole binaries and
spin properties of black hole populations observed by the 3G network.

Black holes are the most compelling explanation for the companions in binary
coalescences discovered by LIGO and Virgo detectors. The tell-tale signature
of a black hole would be present in the quasi-normal mode spectrum of the
merger remnant, whose frequencies and damping times should depend only on the
remnant’s mass and spin. Signature of additional degrees of freedom would be
seen as inconsistency in the remnant’s parameters determined by the different
modes. Certain alternatives to black holes could mimic the quasi-normal mode
spectra, but they could emit additional signals in the form of echoes of the
ingoing radiation reflected from their surface, which could be observable in
the 3G network.

Big Bang cosmology is largely consistent with general relativity but the
accelerated expansion of the Universe in its recent history cannot be
explained by the theory, indicating either its failure or the presence of
exotic form of matter-energy density, of which we know very little.
Observations on galactic to cosmological scale provide unequivocal indirect
evidence for the presence of weakly interacting dark matter, but none has been
directly detected in spite of concerted efforts over the past six decades. The
3G network might detect various forms of dark matter including axionic and
other dark matter fields around black holes and neutron stars, primordial
black holes, etc.

###  1.6 Sources at the Frontier of Observations

The physics of supernova explosion, glitches in the frequency of pulsars and
quakes in highly magnetized neutron stars (or magnetars) are open problems in
astrophysics. Many of these systems will generate GWs that could be observed
with 3G detectors at distances of several million light years for supernovae
and within the galaxy for pulsar glitches and magnetar flares. GW observations
of these systems with the 3G network, enhanced by EM and neutrino
observatories, will allow us to probe extreme astrophysics and address key
questions that have hindered progress in our understanding of the mechanism
behind stellar explosions.

From the observed spectrum of GWs it will be possible to determine the physics
of core collapse supernova: the different phases of the collapse, the nature
of the explosion that dominates the production of GWs and the asymmetry of the
collapse and what triggers that asymmetry. Information about the rotation rate
of the progenitor star is also encoded in the observed signal and it should be
possible to understand how the initial state of the progenitor star determines
the final state of the collapse, a black hole or a neutron star. Such
observations will be greatly aided by all-sky optical and infrared surveys of
the stellar population in nearby galaxies, as well as cosmic rays and
neutrinos.

Isolated neutron stars could emit GWs if they are not spherical and don’t
rotate about their symmetry axis. Indeed, they are persistent sources with the
emission lasting for millions of years. Advanced detectors are not likely to
detect continuous waves from known pulsars, although all-sky blind searches
may reveal hitherto unexpected sources. The 3G network could observe neutron
stars whose polar and equatorial radii differ by no more than 10 to 100
microns. This will provide invaluable information about their crustal
strengths and the equation-of-state of high density nucleons in their outer
cores.

Accreting neutron stars, e.g., in low-mass X-ray binaries, could acquire
quadrupole deformations from the in-falling matter that could lead to a
perpetual source of GWs. Indeed, the 3G network will help resolve if the
accretion torque balanced by the GW back-reaction torque is responsible for
the observed limiting spin frequencies of neutron stars in low-mass X-ray
binaries. The 3G network will also probe the role of magnetic fields in
transient radio emission from magnetars provided the mechanism is caused by
crustal quakes that result in the emission of GWs. This could further
constrain the equation-of-state of neutron star crusts.

###  1.7 Summary

LIGO and Virgo discoveries have ushered in a new era in multimessenger physics
and astronomy. GW observations can be used to probe the nature of ultra dense
matter, reveal quantum chromodynamic phase transitions, study the formation
and evolution of stellar mass black holes from the epoch of the formation of
first stars, measure cosmological parameters, examine phase transitions in the
early Universe, test general relativity in dynamical spacetimes, discover the
nature of dark matter and other exotic compact objects, and explore the
physics of the most violent processes in the cosmos. The mind boggling reach
of the 3G network is difficult to fathom but guarantees serendipitous
discoveries, with the potential to unearth new physics. Indeed, 3G
observatories will operate in a survey mode wherein signals that do not fit
our expectations will be flagged off for further study. The science case for
building a new generation of GW detectors that can probe deep into the cosmos
and observe a variety of different processes is immensely rich and massively
rewarding.

##  Chapter 2 Extreme Matter, Extreme Environments

Science Target Determine the properties of dense matter, discover phase
transitions, and the emergence of quarks.

The discovery of the binary neutron star (BNS) merger GW170817 [1] was a
watershed moment in astronomy and astrophysics. Multimessenger observations of
the source observations provided incontrovertible evidence that BNS mergers
are connected to short-hard gamma-ray bursts (GRBs) [2, 3] and its optical
localization [4] unveiled that they are prolific sites of heavy element
nucleosynthesis [5, 6, 7]. It confirmed that GWs and light travel essentially
at the same speed, and allowed the first measurement of the Hubble constant
using GW standard sirens [8, 9] ushering in a new era in cosmology.
Furthermore, the event enabled the first measurement of the neutron star (NS)
tidal deformability [2, 10] and provided the most robust and stringent
constraints on the NS radius and the equation of state of dense matter under
extreme conditions inaccessible to experiments and first-principles
theoretical calculations [11, 12, 13, 10, 14, 15]. Circumstantial evidence
from the EM counterparts for the formation of a black hole (BH) on a timescale
of tens of milliseconds provided tighter, albeit model-dependent, constraints
on the maximum mass of NSs, and lower bounds on their radii [16, 17, 18].

However, a number of important questions were left unanswered (see Sec. 2.1).
Accurate observations of a diverse population BNS mergers with detectors of
greater sensitivity and bandwidth will be key to shedding light on the nature
of extreme matter in extreme environments produced by the mergers.

Key Science Goals Multimessenger observations of numerous luminous events in
the Universe involving dense matter in extreme environments will uncover
several key puzzles in fundamental physics: • Nature of matter at supranuclear
densities. What are the fundamental properties of the densest matter in the
cosmos? How do quarks and gluons manifest in the cores of the most massive
neutron stars? • Production sites of heavy elements. What elements are
produced in NS mergers and how? Are they able to explain the abundances of
elements heavier than iron in the solar system and in stars? • Formation and
evolution of compact binaries. How do NS binaries form and evolve? What are
their demographics, merger rates, and mass and spin distributions through
cosmic time? • Central engines of short-hard GRBs. What is the role of the
merger remnant and the physics of central engines powering panchromatic EM
counterparts to NS mergers? How do they relate to short GRBs?

Capabilities of Next Generation Detector Networks: The 3G network will compile
a survey of the Universe of a large sample of BNS and NS-BH mergers. Table 2.1
shows the detection capability of 3G observatories compared to the network of
advanced detectors at their design sensitivity. In computing the event rates
the local co-moving merger rate was taken to be 1000 Gpc-3 yr-1 and redshifts
at the epoch of merger were sampled assuming the Madau-Dickinson star
formation rate, with an exponential time delay (an e-fold time of 100 Myr)
between formation and merger [19]. Tens of thousands of well-localized events
detected by the 3G network will provide ample opportunities for EM follow-up
of these mergers as opposed to a handful of them by the current network.

In addition to discovering a great number and diversity of mergers through
cosmic time, the wide band sensitivity of 3G detectors will enable tracking
the full inspiral, merger and post-merger GW signals. These unique
capabilities will help address key science questions on the properties of
dense matter. The 3G network will accurately measure the masses and spins NSs
and determine their long-sought equation of state, probe the merger dynamics,
state of the merger remnant and BH formation, and explore, for the first time,
properties of matter at even greater density and temperature if the remnant
does not promptly collapse to a BH.

BNS Event Rates in 2G & 3G Networks

Table 2.1:  Expected number $N$ of BNS detections per year, the number of events localized to within $1$, $10$ and $100$ deg2 ($N_{1},$ $N_{10}$ and $N_{100}$, respectively) and the median localization error $M$ in square degrees, in a network consisting of LIGO and Virgo (HLV), LIGO, Virgo, KAGRA and LIGO-India (HLVKI) and the 3G network. Network | $N$ | $N_{1}$ | $N_{10}$ | $N_{100}$ | $M$
---|---|---|---|---|---
HLV | 48 | 0 | 16 | 48 | 19
HLVKI | 48 | 0 | 48 | 48 | 7
3G | 990k | 14k | 410k | 970k | 12

The sub-arcsecond localization of the panchromatic EM counterpart will provide
information about environment and geometry of the event, its host galaxy, the
physical state and evolution of the ejected material and the nucleosynthesis
of heavy elements. Thus, the combination of information derived independently
from the GW and EM signals will be immensely powerful to build a complete,
self-consistent astrophysical picture, enable cosmological applications, and
constrain formation scenarios.

###  2.1 Nature of Matter at Highest Densities

Neutron stars are precious laboratories for the subatomic physics of matter
under unique conditions. The multitude of phenomena connected with
multimessenger emissions from BNS mergers is of broad interest to nuclear and
particle astrophysics. Our current understanding of the NS interior is
captured in Fig. 2.1. The theoretical understanding of matter up to densities
present in terrestrial nuclei ($\rho_{0}\simeq 2.5\times
10^{14}\leavevmode\nobreak\ \mathrm{g\,cm}^{-3}$) are fairly advanced and
relevant to the NS crust. However, nuclei dissolve at higher densities
$\rho\gtrsim\rho_{0}/2$ into a uniform liquid of neutrons, with a small
admixture of other particles including protons, electrons, and muons [20]. In
NSs with large masses, densities in the core may be sufficiently high for
exotic states of matter to appear. Furthermore, at densities $\gtrsim
2\rho_{0}$–$3\rho_{0}$ the distance between nucleons becomes comparable to
their size, and their quark sub-structure is expected to manifest and phase
transitions to new states of matter containing deconfined quarks may occur
[21].

Internal Structure of a NS Figure 2.1: Composition of matter in the interior
of a NS predicted by theory. Quark degrees of freedom become important at the
densities encountered in the inner core. The nature of the transition to
matter containing de-confined quarks is unknown.

The nature and location of the transition from hadronic to quark matter
remains unknown, but is a fundamental question with broad implications. The
properties of matter inside NSs directly affect their global characteristics,
masses and radii, motivating significant observational [22, 23] and
theoretical [24, 25, 26, 27, 28] efforts to constrain the properties of NS
matter and measure NS masses and radii. Radio observations of pulsars have
yielded accurate mass measurements of a handful of NSs [23]. The discovery of
a massive NSs with $M\simeq 2$ M⊙ [29, 30, 31] has had far-reaching
implications for the equation of state of dense matter [32]. However, accurate
measurements of the NS radius from X-ray observations have been more
challenging since they rely on poorly tested models of EM emission from or
near the NS surface. Efforts to model and interpret X-ray data from accreting
NSs during bursts, and in quiescence, suggest that NS radii are in the range
$9$–$13$ km [23, 33], albeit with untested model assumptions. For a few
pulsars, NASA’s NICER mission is anticipated to provide reliable radius
measurements, using a different method [22]. Results from the first NICER
observations are promising, although the errors associated with the extracted
NS radius remains large [34, 35].

The 3G will probe the properties of dense matter in a _diverse population_ of
NSs by measuring a variety of matter-dependent GW signatures during the
inspiral phase of BNS systems. These arise from tidal effects, including the
tidal excitation of a NS’s internal oscillation modes [36, 37, 38, 39] that
can provide direct information about phase transitions, rotational
deformations [40], spin-tidal couplings [41, 42], and the tidal disruption of
the NS by a BH companion [43, 44]. The 3G network will measure the radii of
several NSs over a wide mass range including both light and heavier NSs to
within 0.5 to 1 km, and discern subdominant matter effects on GWs. Both these
aspects are critical for measuring the properties of dense matter and
discovering phase transitions. Fig. 2.2 shows a projection of the precision
with which 3G detectors will allow us to measure the NS mass and radius.

The 3G network will further open an exceptional window onto fundamental
properties of _matter in a completely unexplored regime_ , at higher
temperatures and yet greater densities than encountered in NSs, which is
accessible only during the merger and post-merger epochs in BNS collisions.

Measuring NS Radius Figure 2.2: The plot shows $90\%$ credible region for
eight NSs with masses in the range $1.1\mbox{--}1.6M_{\odot}$ in four
binaries, optimally oriented at a distance of $400\leavevmode\nobreak\ {\rm
Mpc}$, with signal-to-noise ratio of $100\mbox{--}140$ in a 3G detector.
Crosses (curves) represent the masses and radii (six equations of states)
chosen for the simulation. In this example, the NS radius is measured to
within $0.5\mbox{--}1\leavevmode\nobreak\ {\rm km}$.

The merger outcome depends on the companion masses and the equation of state
of NS matter [45, 46, 47, 48]. Above a critical total mass of the binary the
merger will result in prompt collapse to a BH, while for very low-mass
progenitors a stable remnant may form. For a wide range of parameters, the
merger outcome is a short-lived hypermassive NS that involves complex
microphysics and generates a significant amount of GWs [49, 50, 51, 52, 53,
54, 55, 56, 57, 58] ultimately collapsing to a BH. The rich GW signals from
the merger and post-merger regimes have frequencies in the range 1–5 kHz and
are thus difficult to measure with advanced detectors; detailed studies of the
complex physics driving the dynamics of NS binary mergers and beyond are a
major unique capability of the 3G detector network.

Various phases of strongly interacting matter that will be uniquely accessible
with 3G detectors are depicted in Fig. 2.3, which focuses on the regimes
relevant to NS binaries that are complementary to those explored by heavy ion
collisions. Matter encountered during BNS mergers, shown as light-green shaded
region, explores a large swath of the phase diagram of dense matter. The 3G
network will enable unprecedented measurements of the new physics encountered
during the coalescence and post-merger epochs, with EM and neutrino
counterparts providing complementary information to obtain a deeper and more
complete understanding of extreme states of matter.

In summary, observations by the 3G network will shed light on many critical
questions about the nature of NSs and the fundamental subatomic physics of
matter: Are NSs composed solely of similar constituents as nuclei on earth or
do they contain condensates of exotic particles or quark matter phases? Do NS
mergers produce novel phases of matter not realized inside nuclei and heavy-
ion collisions? What is the nature of the transition from nuclear to quark
matter? How do nuclear reactions and neutrinos shape NS merger dynamics?

Phase Diagram of Dense Matter Figure 2.3: The phase diagram of dense matter
conjectured by theory and focusing on the regime relevant for NSs,
complementary to the parameter space probed by heavy ion collisions. The
figure shows approximate boundaries between different phases of matter and the
most relevant degrees of freedom. The regions occupied by cold NSs (blue
shaded region) and the those encountered during the merger (green shaded
region) are also shown.

###  2.2 Nucleosynthesis in Neutron Star Binary Mergers

A long-standing puzzle in astrophysics is how the elements heavier than iron
came into being. About half of these elements are believed to have been
created by a nuclear process of rapid neutron capture (the r-process) but it
is unclear which astrophysical sites are the main contributors. GW170817 and
its associated thermal EM counterpart provided the first direct identification
of a NS merger as a prolific site of r-process nucleosynthesis [59]. However,
determining the degree to which NS mergers contribute to cosmic chemical
abundance and evolution will require a more extensive sample of the rates,
locations, timescales, and nucleosynthetic yields of the various types of
merger events.

Heavy elements can be synthesized in BNS or NS-BH tidal disruptions when
clouds of neutron-rich material are expelled, either dynamically during the
merger or through winds blown off the remnant accretion disk. The subsequent
radioactive decay of the freshly synthesized elements powers a thermal
ultraviolet/optical/infrared EM transient called a kilonova. The brightness
and color of the kilonovae are diagnostic of both the total mass of r-process
elements and the relative abundance of lighter to heavier elements [60].

Whereas historical studies of chemical evolution have relied on observing
fossil traces of r-process elements mixed into old stars, multimessenger
observations provide the unique opportunity to study heavy element formation
at its production site and to determine how the initial conditions of an
astrophysical system map to the final nucleosynthetic outcome. Answering the
basic question of the extent to which BNS and NS-BH mergers are the site of
r-process production will require multimessenger observations of a large
sample of events. GW measurements with the 3G network will pin down the rate
of mergers and the binary properties, such as the binary type (BNS or NS-BH),
companion masses, spin–orbit alignment, and the merged remnant lifetime, while
optical/infrared photometry of the associated kilonovae will determine the
average r-process yields and probe the relative abundance distribution of
heavy elements. These observations will also illuminate the key physics
driving the r-process and kilonova, such as the equation of state of dense
matter, the fundamental interactions of neutrinos and the magneto-
hydrodynamics of accretion.

Statistical studies of multimessenger observations will reveal how r-process
production depends on host galaxy type, location and redshift, allowing us to
piece together the history of when and where the heavy elements were formed
over cosmic time. Such studies can determine the distribution of delay times
between star formation and mergers, thereby addressing whether some of these
mergers occurred promptly enough to explain the enrichment of the oldest metal
poor stars and the extent to which compact binaries receive strong kicks that
may expel them from their host galaxies, a factor that is important for
understanding whether mergers can explain the unusually high r-process
enhancement seen in some dwarf galaxies [61].

In the era of 3G detectors, optical kilonovae will be detectable by the Vera
Rubin Observatory out to 3 Gpc and infrared characterization photometrically
by WFIRST/Euclid and spectroscopically by JWST/GMT/TMT/E-ELT would be out to
$1$ Gpc ($z<0.2$). The multimessenger information about these event will
enable answering questions such as: How nuclear reactions and neutrinos shape
NS merger dynamics and nucleosynthesis? How do the properties of nuclei that
are far from stability impact the EM emission from material ejected during NS
mergers? How do the progenitor properties impact the nucleosynthesis and
kilonovae?

###  2.3 Formation, Demographics and Merger Sites of Compact Binary Mergers

Observations of NS binary merger systems systems are essential to advance our
understanding of how nature assembles these systems–either via standard
(isolated) binary star evolution or via dynamical encounters in dense stellar
environments. Precise measurements of NS masses and spins in these systems
across cosmic time will provide key evidence for their origin in different
types of supernova explosions and fossil records of close binary progenitor
star interactions and accretion history after birth. Any signs of NS masses
being different in NS-BH mergers compared to BNS mergers will yield crucial
information on their formation process and the evolution of massive stars.

A key question about compact binary mergers is their demographics, as this
could reveal their formation mechanism. Localization of merger events to less
than galactic scales ($\sim 30$ kpc) is essential to unambiguously infer
associations of mergers with their host galaxies. Without an EM counterpart
the vast majority of GW events will have error boxes that greatly exceed the
typical radii of potential host galaxies. The census of the binaries, their
locations, and environments will provide deep insights into the formation and
evolution of NS binaries and their connection with the progenitor stars [62,
63, 64].

EM follow-up of NS binary mergers will be critical in pinning down host
galaxies. For binaries involving a NS and a BH with a mass ratio that is not
too large, depending on the BH’s spin, the NS may get tidally disrupted. The
debris may result in accretion disk around the BH and lead to EM counterparts
that might rival the absolute visual magnitude of the GW170817 kilonova, and,
unless they occur in globular cluster cores, will be detectable out to $z=0.5$
in the reddest filters.

Based on our current understanding, galaxies are assembled by the merger of
smaller proto-galaxies and star formation peaks near $z\sim 2$ [65].
Identification of kilonovae beyond $z\sim 0.5$ requires hour-long integrations
on 8m class facilities such as LSST or Subaru, rendering the identification of
the host galaxies of binary NS mergers near the peak of star formation more
challenging in the absence of a gamma-ray burst jet pointing towards the
Earth, even with ELTs. Nevertheless, at redshifts $z<0.5$ 3G detectors will
work in concert with astronomy facilities to enable thousands of host galaxy
identifications from NS binary mergers where the kilonova counterpart is
observable. At larger distances, the identification will be possible only
through the detection of an associated gamma-ray burst afterglow, which can be
much more luminous than a kilonova if the jet is directed towards the Earth.

###  2.4 Jet Physics in Neutron Star Binary Mergers

Relativistic explosions and compact-object mergers can generate collimated,
energetic jets of fast-moving material and radiation. Prior to GW170817, our
understanding of jet physics came from studies of gamma-ray bursts, active
galactic nuclei and X-ray binaries. Multimessenger observations provide an
entirely new perspective on this topic. For instance, the panchromatic study
of GW170817 revealed that there was both a narrow ultra-relativistic jet [9,
66, 67, 68] and a wide-angle mildly relativistic cocoon from surrounding
material ejected during the merger [69, 7, 70]. This event opened up many
questions for future observations to answer. Specifically, what is the
connection to the class of cosmological short hard gamma-ray bursts? Does a
wide-angle mildly relativistic cocoon always accompany a binary NS merger?
Does the jet always successfully escape the cocoon or is it sometimes choked?
How do the observed jet properties vary as a function of viewing angle, mass
ratio, hypermassive NS lifetime, remnant spin, and ejecta mass? Do mergers
produce prompt EM signals or even precursors? What is the distribution of the
time delays between the EM and GW signal arrival times? What are the
characteristics of a jet from a NS-BH merger? A census of NS binary mergers,
and full GW and EM coverage of the signals, joint multimessenger parameter
inference will be key in understanding the physical origin of jets, ubiquitous
around relativistic sources. For the first time, a direct measurement of the
BH spin in a source emitting a collimated jet, will enable to establish the
close correlations between the jet power, the spin and the inflow rate from
the debris disk, which determines the conditions for launching the jet. The
sensitivity of gamma-ray, X-ray and radio telescopes will enable studying jet
physics out to 500 Mpc, thus requiring a sample of the order of a thousand
events localized to better than few square degrees to map the full parameter
space provided by the 3G network.

Facilities for Observing EM Counterparts to GWs

Table 2.2: Present ($P$) and future ($F$) EM facilities that are able to observe faint/distant counterparts to GWs. Detection Limit (DL, 1 hr exposure time) for UV, optical, and near-IR facilities are expressed in AB magnitudes, for X-rays in $10^{-16}\,\rm erg\,s^{-1}\,cm^{2},$ and for radio in $\mu$Jy. Distance reach (D in Mpc) of facilities for GW170817-like events are also shown. | Facility | DL | D
---|---|---|---
Gamma-rays |  Fermi $P$ | S/N 5 | 80
|  AMEGO $F$ | S/N 5 | 130
|  Swift $P$ | S/N 5 |  $\sim$80
|  Chandra $P$ | 30 | 150
X-rays |  ATHENA $F$ | 3 | 480
|  Lynx $F$ | 6 | 450
|  STROBE-X $F$ | S/N 5 | 120
UV |  HST (im) $P$ | 26 | 2000
|  HST (spec) $P$ | 23 | 400
Optical |  Subaru $P$ | 27 | 3200
Imaging |  LSST $F$ | 27 | 3200
IR |  WFIRST $F$ | 27.5 | 4800
Imaging |  Euclid $F$ | 25.2 | 1700
| Facility | DL | D
---|---|---|---
| Keck/VLT | 23 | 500
| Gemini Obs. | 23 | 500
Optical |  GMT $F$ | 25 | 1265
Spec. |  TMT $F$ | 25.5 | 1592
|  E-ELT $F$ | 26 | 2005
| Keck/VLT | 21.5 | 481
Infrared |  GMT $F$ | 23.5 | 762
Spec. |  TMT $F$ | 24 | 960
|  E-ELT $F$ | 24.5 | 1208
Radio |  VLA (S) $P$ | 5 | 91
ATCA (CX) $P$ | 42 | 51
ngVLA (S) $F$ | 1.5 | 353
SKA-mid (L) $F$ | 0.72 | 634

###  2.5 Outlook for Extreme Matter and Extreme Environments

Observations of BNS and NS-BH mergers with a network of 3G detectors will
transform our understanding of the fundamental properties of matter in
unexplored regimes of density and temperature and, in conjunction with EM
facilities, will address longstanding questions about the formation of heavy
elements in the universe, the central engines of highly energetic EM
transients, and the formation and evolution of NS binary systems.

Science Requirements The unique capabilities of 3G detectors required to
accomplish these science goals are: • an order-of-magnitude greater
sensitivity than 2G detectors enabling observations of the NS binary
population in the cosmos and measurements of loud-source properties with
exquisite accuracy, • a wider frequency range than 2G detectors that will
allow tracking the entire GW signals from the inspiral through the merger,
tidal disruption and beyond, and • synergies with panchromatic EM facilities,
that will be critical to fully capitalize on the rich multimessenger science
potential of these sources for cosmology, fundamental physics, and
astrophysics.

##  Chapter 3 Observing Stellar-mass Black Holes Throughout the Universe

Science Target Reveal merging black holes across the cosmos and _search_ for
seeds of supermassive black holes.

Merging binary black holes are sources unique to GW astronomy—they are the
most frequently observed sources to date. We now know that binary black holes
(BBHs) form ubiquitously in galaxies and so far appear to be completely dark.
These mergers are unrivalled laboratories for testing extreme gravity, and
exquisite astronomical sources for gaining insight into the origin and
evolution of massive stars in the Universe. With a leap in sensitivity and
increased frequency bandwidth, the 3G network will observe them back to the
early Universe, chart how the population evolves with time, discover a broader
range of masses, and connect stellar-mass black holes (BHs) with the
supermassive BHs (SMBHs) found in the centres of galaxies, obtain precision
measurements of BH properties, and finally resolve the mysteries of their
formation. GW astronomy is perfectly suited to studying BHs, and with 3G
detectors we would achieve a complete picture of the family of stellar-mass
BBHs.

Key Science Goals The 3G network will uncover BBHs throughout the cosmos, back
to the beginning of star formation and detect new sources, if they exist,
beyond stellar-mass binaries, such as intermediate-mass BBHs. • Discover BBHs
throughout the Universe. What is the merger rate as a function of cosmic time
and how does it relate to the star formation rate, metallicity and galaxy
formation and evolution? • Reveal the fundamental properties of BHs. What are
the mass and spin demographics of BHs throughout the Universe? Are they
correlated and do they evolve with redshift? What do they reveal about the
formation and evolutionary origin of BHs? • Uncover the seeds of SMBHs. GW
observations have proven that intermediate-mass BHs can form at least from BBH
mergers. The 3G network promises to explore their population, reveal if
intermediate-mass BH mergers occur in nature and serve as the long-sought
seeds of SMBHs?

The first three observing runs of Advanced LIGO and Advanced Virgo have
yielded the discovery of _more than 50_ BBH systems. Already these detections
have revolutionized the astrophysics of stellar-mass BHs [71, 72, 73, 74, 75]
and provided first new tests of general relativity [76, 77, 78, 79, 80].
Through the end of the 2020s, the current advanced detector network will
continue to be enhanced as sensitivities reach design goals and a new detector
in Japan, KAGRA, comes online [81, 82]. In the BBH domain, we will be able to
detect a pair of $10M_{\odot}$ BHs out to a cosmological redshift of $z\simeq
1$ when the Universe was $6\leavevmode\nobreak\ \mathrm{Gyr}$ old [82]. The
annual BBH detection rates are forecast to be several hundreds of mergers and
science benefits will compound through accumulated observing time and growing
detected samples [83, 84, 85, 86, 87, 88].

Beyond this horizon, step-wise sensitivity improvements with the next
generation of ground-based GW observatories will be required if we are to
pursue major science questions that cannot be answered by the current and
near-term GW facilities [e.g., 89, 90]. Current-generation GW detectors are
able to provide constraints on the merger-rate densities in the local Universe
and broad constraints on component masses [72, 91]. However, precise
measurements of, for example, spin magnitudes and tilts are of paramount
importance to understand the origin and the evolutionary physics of binary
systems [83, 92, 93, 84, 85, 94, 95, 96]. This information is essential to
obtain insights on the formation channels of compact binaries. So far we have
been surprised by the properties of individual exceptional sources, but the
population constraints are too weak to distinguish among formation path
possibilities. We highlight here how 3G GW ground-based detectors will enable
us to survey deeper, to observe a wider range of frequencies, and to make more
precise physical measurements; how observations can be synergistically
combined between 3G and space-based GW observatories, and how these results
will be transformational in the study of BBH astrophysics.

###  3.1 A survey of BHs throughout cosmic time

With a 3G detector network, for the first time, we will detect BBH mergers at
redshifts beyond $z\sim 1$ and we will measure the evolution of the BBH merger
rate out to redshifts of $z\gtrsim 10$ when the Universe was
$<500\leavevmode\nobreak\ \mathrm{Myr}$ old [82, 88, 19]. GW astronomy would
thereby gain a synoptic view of the evolution of BHs across cosmic time,
beyond the peak of the star-formation rate, which took place at $z\sim 2$ when
the Universe was $3\leavevmode\nobreak\ \mathrm{Gyr}$ old [65], back to the
cosmic dawn around $z\sim 20$ when the Universe was only
$200\leavevmode\nobreak\ \mathrm{Myr}$ old and the first stars were forming in
pristine dark matter halos.

Measurements of the merger rate as a function of redshift combined with high
fidelity measurements of the BH physical parameters will enable conclusive
constraints on the BBH formation channels. Stellar-origin BH formation tracks
cosmic star formation [97, 98, 99, 100, 101, 102], while the density of
primordial BHs is expected to be independent of the star formation density
[103, 104]; different binary formation channels are predicted to lead to
different distributions of delay times between formation and merger [105, 106,
107, 108, 109, 86, 110, 111, 112, 113, 114]. Therefore, determining the merger
rate as a function of redshift provides a unique insight into the lives of
binary BHs. _Only next-generation GW detectors can survey the complete
redshift range of merging BBHs and provide a sufficiently large catalog of
detections to constrain the full BBH population and their origins_.

Sensitivity Required to Observe Cosmic Binary Black Holes Figure 3.1: Colour
maps show the boost factor relative to the LIGO A+ design
$\beta_{\mathrm{A+}}$ required to see a binary with a given total source mass
$M=m_{1}+m_{2}$ out to given redshift. The colour bar saturates at
$\log_{10}\beta_{\mathrm{A+}}=4.5$; some high-mass systems at high redshift
are not detectable for any boost factor as there is no signal above
$5\leavevmode\nobreak\ \mathrm{Hz}$. Panels are for mass ratios
$q=m_{2}/m_{1}=1$ (left) and $q=0.1$ (right). The blue curve highlights the
reach at a boost factor of $\beta_{\mathrm{A+}}=10$. The solid and dashed
white lines indicate the maximum reach of Cosmic Explorer [90] and the
Einstein Telescope [89], respectively; sources below these curves would be
detectable.

To capture BBH mergers across the stellar mass spectrum (up to total masses of
$M=m_{1}+m_{2}\simeq 200M_{\odot}$) all the way back to the end of the
cosmological dark ages ($z\simeq 20$), a major advance in GW detector
sensitivity is required. This cannot be delivered by the maximal sensitivity
planned for the current ground-based detector facilities. We quantify this
sensitivity step by the boost factor $\beta_{\mathrm{A+}}$ relative to the
LIGO A+ design [115] between $5\leavevmode\nobreak\ \mathrm{Hz}$ and
$5\leavevmode\nobreak\ \mathrm{kHz}$ (and no sensitivity outside this range).
In Figure 3.1, we show this boost factor, required to detect an optimally-
oriented, overhead binary at a signal-to-noise ratio (SNR) of $8$, as a
function of the binary’s total mass and redshift. The boost factors
$\beta_{\mathrm{A+}}$ needed to acquire a complete census of BBH mergers
throughout the Universe are well within the design aspirations the 3G network;
for these specific sensitivity assumptions, BBH mergers of total mass $M\sim
10$–$40M_{\odot}$ can be detected out to $z\sim 10^{2}$.

Observations of the cosmological distribution of coalescing binaries would
complement planned EM surveys designed to study stars and stellar remnants
back to cosmic dawn [116, 117, 118, 119, 120], as well as millihertz GW
observations made by the Laser Interferometer Space Antenna (LISA) [121],
which can observe systems ranging from local stellar-mass binaries (days to
years before they enter the frequency range of terrestrial detectors) [122,
123] to SMBH systems in the centres of galaxies [124, 125]. In X-rays SMBHs
are detectable due to gas accretion in galactic nuclei. X-ray observatories
like Athena [126] and the mission concept Lynx [127] would detect SMBHs back
to high redshift ($z\gtrsim 7$); Lynx would observe $10^{3}M_{\odot}$ BHs to
$z\sim 5$ and $10^{2}M_{\odot}$ BHs to $z\sim 2$, while Athena will survey
these in the nearby Universe. Next-generation GW detectors have the unique
potential to observe stellar-mass BH systems all the way back to the early
Universe.

###  3.2 Expanding the BH mass spectrum

EM astronomy has benefited enormously from advancing observing facilities to
cover an expanded range of frequencies. These enable new probes of previously
known sources, and allow for the discovery of new types of previously
unobserved sources. _3G GW detectors have the unique capability to push the
frequency range down to $\simeq 1\leavevmode\nobreak\ \mathrm{Hz}$ and up to
$\simeq 5\leavevmode\nobreak\ \mathrm{kHz}$_, while improving performance
across the band in between.

The merger frequency for a coalescing binary scales inversely with the mass of
the binary, hence observing at lower frequency opens up the potential of
detecting more massive BHs. The first intermediate-mass BH (mass in excess of
$100M_{\odot}$) has already been observed as the result of a BBH merger [128],
but there may be multiple formation paths for these BHs. Reaching down to
frequencies of $\simeq 1\leavevmode\nobreak\ \mathrm{Hz}$ is the most robust
means to chart the population of intermediate-mass BHs, and discover any
mergers of intermediate-mass BHs—which may be the process through which SMBHs
form [129, 130, 131, 132]. SMBHs are observed up to redshift $z=7.54$ [133] as
quasars, at lower redshifts as active galactic nuclei [134], and today in
massive galaxies in their quiescent state [135], and cover a mass range from
$\sim 10^{4}M_{\odot}$ [136, 137, 138, 139] up to $>10^{10}M_{\odot}$ [140,
141, 142]. SMBHs may have light seeds ($\sim 10^{2}$–$10^{3}M_{\odot}$),
formed from massive stars in low metallicity halos which evolve into BHs
beyond the pair instability gap [143], or heavy seeds, formed from
supermassive (proto)-stars of $\sim 10^{4}$–$10^{6}M_{\odot}$ growing through
continued and fast accretion within their birth clouds, which eventually
collapse down to BHs [144, 145, 146, 147, 148, 149]. In particular, the
observation of high-redshift BHs with mass $\gtrsim 100M_{\odot}$, beyond the
(pulsational) pair-instability supernova mass gap (where supernova explosions
are hypothesised to completely disrupt the star leaving behind no remnant)
[150, 151, 152, 153, 154, 155], would be key to understand not only the
properties of very massive ($\gtrsim 250M_{\odot}$) metal-poor stars [156,
157], but also the assembly of the first massive BHs in the Universe [158,
159, 160, 161, 162].

In Figure 3.2, we illustrate the importance of sensitivity in the
$1$–$10\leavevmode\nobreak\ \mathrm{Hz}$ regime. Even with detectors sensitive
to $3\leavevmode\nobreak\ \mathrm{Hz}$, we see only one cycle of a
$100M_{\odot}+100M_{\odot}$ circular binary with non-spinning components at
$z=10$ before merger. This system is not observable above
$10\leavevmode\nobreak\ \mathrm{Hz}$. Therefore, the objective to observe the
most massive BBHs of stellar origin and the potential seeds of SMBHs in the
Universe’s early history requires new detectors sensitive to currently
inaccessible frequencies below $\sim 10\leavevmode\nobreak\ \mathrm{Hz}$.

Waveform from a Binary Black Hole Coalescence Figure 3.2:  Left: The waveform
from the final stages of inspiral, merger and ringdown of a
$100M_{\odot}+100M_{\odot}$ BBH at a redshift of $z=10$. Highlighted is the
time evolution of the waveform from $3$, $5$ and $7\leavevmode\nobreak\
\mathrm{Hz}$. Right: Requirements on the low-frequency noise power spectrum
$S_{n}(f)$ necessary to detect an overhead, face-on
$100M_{\odot}+100M_{\odot}$ BBH merging at $z=10$. We assume a power-law form
$S_{n}(f)\propto f^{\alpha}$ extending down to a minimum frequency
$f_{\mathrm{min}}$ with the specified normalization $S_{10}$ at
$f=10\leavevmode\nobreak\ \mathrm{Hz}$.

The detectability of intermediate-mass BHs places requirements on low-
frequency sensitivity. We can model the low-frequency noise power spectral
density of the detector as a power-law
$S_{n}(f)=S_{10}(f/10\leavevmode\nobreak\ \mathrm{Hz})^{\alpha}$ and assume
that the power law extends to some minimal frequency $f_{\mathrm{min}}$, below
which the detectors have no sensitivity. In Figure 3.2, we show the
combination of power law $\alpha$, minimum frequency $f_{\mathrm{min}}$ and
the normalisation $S_{10}$ necessary to detect an optimally located and
oriented merger of two $100M_{\odot}$ intermediate-mass BHs at $z=10$. There
is a trade-off between the power-law slope, minimal frequency and overall
normalization, such that a range of specifications can fulfill the science
requirements.

###  3.3 High-precision measurements of binary properties

A leap in sensitivity combined with the increased frequency bandwidth of the
3G detectors will enable high-precision measurements of the properties of
individual binaries [163, 164, 165]. Parameter uncertainties are inversely
proportional to the SNR [166]. The increase in SNR made possible by the
greater sensitivity will lead to exquisite measurements of the loudest events.
Increased bandwidth enables the coalescence to be tracked for a longer time,
improving estimates of quantities like the spins. Masses, spins, merger
redshifts, orbital eccentricities and (where possible) associations with host
galaxies all give complementary insights into binary physics. High-precision
measurements of individual systems allow us to make detailed studies of their
origins and fundamental physics [167, 168, 169, 170, 171, 172]. Combining many
events together lets us study the properties of the population. _The unique
and critical advantage of BBH observations with the 3G network is the
combination of high-precision measurements for a very large number of detected
sources_ , something that cannot be delivered by the current detectors.

As an example, consider a highly precise reconstruction of the BH mass
spectrum. At high masses, a gap is predicted to exist between $\sim
50M_{\odot}$ and $\sim 130M_{\odot}$ due to (pulsational) pair-instability
supernovae [173, 152, 154, 155], although nature has some ways to form BHs in
it [128]. At lower masses, there is potentially a gap between the maximum
neutron star mass and the minimum stellar BH mass [174, 175, 176, 177, 75].
Determining the precise bounds for these gaps would provide insight into the
mechanics of supernova explosions [178, 179, 180, 181], insights into the
neutron star equation of state [182, 11, 16, 183, 10, 184, 185, 186], and even
details of nuclear reaction rates [155, 187]. It can be shown that: (i) for
the high-mass gap, if the desired accuracy on the mass gap boundary
measurement is $\sigma_{g}\sim 1M_{\odot}$, with a conservative individual
mass uncertainty for near-threshold detections of order $\sigma_{m}\sim
10M_{\odot}$, $N\gtrsim 500$ detections are required; (ii) for the low-mass
gap, $\sigma_{g}\sim 0.3M_{\odot}$ and $\sigma_{m}\sim 3M_{\odot}$, would
require $N\gtrsim 1500$ BBH detections. To provide robust answers to questions
regarding massive star evolution and BBH formation, we need to trace the
dependence of the boundaries of the mass gaps on metallicity and hence
redshift. Therefore, it is desirable to observe $\sim 1000$ sources in each
redshift bin of width $\Delta z=0.1$, since we may expect knowledge of the
star formation rate and metallicity distribution to be available at this
resolution on the timescale of the 3G network [65]. Such observations would
provide $\sim 3\%$ fractional accuracy on the merger rate per redshift bin,
sufficient to determine the redshift evolution of the rate, and constrain
details of the binary evolution at that redshift [87, 86].

Expected BBH Merger Rate Figure 3.3: Expected rate of BBH detections
$R_{\mathrm{det}}$ per redshift bin as a function of $A+$ boost factor
$\beta_{\mathrm{A+}}$, for $z=[0.4,0.5]$, $z=[1,1.1]$, $z=[2,2.1]$,
$z=[3,3.1]$. Constant BBH merger rate densities of $53$ ($112$, $24$)
$\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ are shown with solid (dashed, dotted)
curves, assuming equal component masses distributed according to $p(m)\propto
m^{-1.6}$ [72].

With this in mind, we plot the number of expected BBH detections for a next-
generation detector as a function of its boost factor relative to A+ in Figure
3.3. This assumes a BBH merger rate that does not evolve in redshift and is
roughly consistent with current GW observations [72]. From this, the target of
$\sim 1000$ detections per redshift bin is achievable with boost factors of
$\beta_{\mathrm{A+}}\sim 10$ after only $2$ years of observing time. These
factors are possible only with next-generation GW detectors.

We note that observing across a broader range of frequencies gives a more
complete picture of BBH properties. The precession of component spins
misaligned with the orbital angular momentum occurs over many orbits [188,
189]. Its imprint is easier to discern over longer inspirals, and hence
becomes more apparent with low-frequency data. Orbital eccentricity is rapidly
damped through GW emission [190].This means that it is near immeasurably small
for current GW detectors [191, 192, 193], but reachable for 3G detectors. Both
the spins and the orbital eccentricity are indicative of the formation
channel; enabling their measurement for large samples will have a
transformative effect on our ability to answer questions about BBH origins.

###  3.4 Multiband gravitational-wave observations

Joint observations of GW events by LISA at millihertz frequencies and 3G
detectors at higher frequencies maximises their science potential. If LISA had
been observing in 2010, it would have detected GW150914 years before it was
observed by LIGO [122]. LISA will potentially see up to hundreds of stellar-
mass BBH mergers of $M>20$–$30M_{\odot}$, up to $z\approx 0.3$ [122, 194]. A
small fraction of these will sweep across the detector band within few years
that will eventually be detected by ground-based detectors. Multiband
observations enables unrivalled measurements of BBH properties.

LISA would provide a precise measurement of the system’s eccentricity to a
precision of $\Delta{e}<0.001$ [195], sky localization to
$0.1\leavevmode\nobreak\ \mathrm{deg}^{2}$, and time to coalescence within few
seconds, several weeks prior to coalescence [122]. This enables EM telescopes
to be pointed in the right direction before the merger, permitting a much
deeper coverage from radio to gamma-ray than what is possible without any
early warning. Alternatively, one can use the information extracted by the 3G
network to dig out sub-threshold LISA events [196]. From an astrophysical
standpoint, the eccentricity information from LISA can be combined with the
spin measurement from 3G detectors to better constrain different formation
channels [197, 198, 199]. Multiband observations will also facilitate tests of
general relativity [200, 201, 202, 203] by enhancing the sensitivity to
specific deviations arising in the long inspiral as predicted, for example,
from dipole radiation not predicted in general relativity [204].

Figure 3.4 shows the cosmological growth of the earliest light and heavy seeds
that transit into the supermassive domain, inferred using a semi-analytical
model for the formation of quasars at $z=6,$ $z=2$ and $z=0.2$ [205]. Binaries
of light seeds ($\sim 10^{2}\,M_{\odot}$) are accessible to the 3G network
with an SNR of 10–20 at $6<z<15.$ They then enter the LISA domain with larger
SNRs as they grow to a few $10^{4}\,M_{\odot}.$ Mergers above
$10^{5}\,M_{\odot}$ come from at least one heavy growing seed in the binary,
lighter mergers arise from the light-seed population. Combining the
observations in the two different frequency domains will provide the first
ever census of coalescing BBHs forming in the Universe. The comparison between
the detection rate between light and heavy seed BHs in the two GW bands will
be instrumental in determining, at statistical level, the relative
contribution of light and heavy seeds in building up the population of SMBHs,
and the role of mergers versus accretion in determining their growth. Figure
3.4 highlights that intermediate-mass BHs are a prime multiband GW astronomy
target [206, 207]. As well as both 3G and space-based detectors being able to
see the same intermediate-mass BH binary signal at different phases in the
inspiral, two GW bands allow the intermediate-mass BH population to be
explored in different regimes. While LISA will be sensitive to mergers of
$M\geq 10^{3}M_{\odot}$ binaries out a redshift of $z>20$, 3G detectors will
be able to access $M\sim 100M_{\odot}$ populations at comparable redshifts.
_Multiband GW observations will quantify the continuity between the stellar-
mass, intermediate-mass, and SMBH populations_.

BBH Mergers in 3G and LISA Figure 3.4: Contours of constant SNR in the space
of redshift (or cosmic time) and total-mass assuming equal-mass binary
companions. The plot also shows the cosmological growth of light seeds that
formed when the Universe was less than 0.3 Gyr old ($z>13$), and the growth of
heavy seeds that form at $z\sim 12.$ Seeds growing through merger transit into
the supermassive domain and form quasars at $z=6$ (triangles), $z=2$ (squares)
and $z=0.2$ (circles) [205]. Mergers above $10^{5}\,M_{\odot}$ host at least
one heavy seed. Mergers lighter than $10^{5}\,M_{\odot}$ come from only the
light seed population.

###  3.5 Outlook for black hole gravitational-wave astronomy

The 3G network will enable the measurement of the cosmological evolution of
the mass and spin distributions of BBHs and probing their dependence on star
formation history and metallicity evolution with redshift. They will make
robust discovery of intermediate-mass black holes, if they exist, and reveal
the boundaries of any mass gaps. The precise measurements of physical
properties for large numbers of BH systems, back to the cosmic dawn, would
lead to constraints on the physics of massive star evolution in single and
binary systems, and to place bounds on the different formation channels of
merging BBHs. Additionally, 3G observations could solve the long-standing
mystery of the nature of SMBHs’ seeds. 3G data would complement those from
future EM and space-based GW observatories, enabling the maximum scientific
return from these facilities. We have an unparalleled opportunity to advance
the frontiers of stellar astrophysics, the fundamental physics of compact
objects, and the formation mechanisms for the entire spectrum of BHs.

Science Requirements The 3G network will transform our BH studies by enabling
cosmological probes of their formation across cosmic time: • an improvement of
a factor of 10-20 in strain sensitivity will allow us to probe the complete BH
population to the edge of the universe, • reaching down to frequencies of
about 1 Hz is needed to detect a population of intermediate-mass BHs, and
quantitatively probe mergers of such BHs and uncover their link to LISA
sources and SMBH growth, and • both the leap in sensitivity and expansion to
low frequencies are needed for precise BBH properties, masses, spins, and
possibly eccentricities, to firmly uncover their formation origins.

##  Chapter 4 Cosmology and the Early History of the Universe

Science Target Investigate the particle physics of the primeval Universe and
probe its dark sectors.

Gravitational waves (GWs) offer unique new probes of the early universe and
its composition—the weakness of gravity relative to other known forces implies
that GWs decoupled very early from the primordial plasma in the Universe, a
fraction of a second after the Big Bang. Detection of such waves would provide
unique opportunities to study the evolution of the very early Universe and of
the physical laws that apply at very high energy scales, inaccessible in
traditional laboratories. Particle physics processes that drove inflation and
phase transitions in the early Universe would leave imprints in the form of
spectral, spatial, and polarization properties of the stochastic GW
background. In the more recent history, merging neutron star (NS) and black
hole (BH) binaries generate signals that precisely determine the luminosity
distances of the binaries, independently of the cosmic distance ladder. Such
coalescing binaries can be used as _standard sirens_ to measure the expansion
and acceleration rates of the Universe as a function of redshift, thereby
inferring fundamental properties of the dark sectors and of gravity itself.

Key Science Goals Future GW observations will enable exploration of particle
physics, _early Universe_ , and cosmology: • Standard Siren Cosmology. What is
the precise value of the Hubble constant? Is dark energy fully described by a
cosmological constant, or does its equation-of-state vary with redshift? •
Early Universe. What particle physics laws and energy scales drove the
Universe’s early evolution? How did it transition from one evolutionary phase
into another and to the present Universe? • Modified Theories of Gravity. Do
GWs propagate from their sources in the same way as EM waves do? How do
modified theories of gravity affect the propagation of GWs from their sources?

Gravity assembles structures in the Universe from the smallest scale of
planets to the largest scale of galaxy clusters and the Universe itself. GW
observations can, therefore, elucidate the Universe’s evolution and its
constituents, complementary to the EM, neutrino, and particle observations.
Indeed, GW observations forever changed the role of gravity in our exploration
of the Universe. In particular, the multi-messenger nature of GW170817 [2, 59]
generated a treasure trove of data ushering in a new era in cosmology [8].

General relativity (GR) completely determines the time evolution of the
amplitude and frequency of GWs generated by binaries of NSs and BHs. Matched
filtering the GW data with the predicted GR waveform readily infers the
luminosity distance to the binary’s host galaxy [208]. Thus, coalescing
binaries have been hailed as _standard sirens_. Just like the traditional
standard candles (e.g. type Ia supernovae) they provide a tool for measuring
the dynamics of the Universe, but are not susceptible to the systematic biases
of the cosmic distance ladder. Standard sirens can be used to make completely
independent measurement of the Universe’s expansion rate as a function of
redshift and to infer cosmological parameters describing the dark sector.

The measured compact binary merger rates [72, 1] imply that future detectors
will observe a stochastic background formed from the astrophysical population
of binaries at cosmological distances [71, 209]. Such observations will reveal
the history of star formation from a time when the Universe was still
assembling its first stars and galaxies. Buried under this background could be
stochastic signals of primordial origin (see, e.g., [210, 211, 212, 213, 214,
215, 216, 217, 218, 219, 220]) that provide insights into the physics and
energy scales of the earliest evolutionary phases in the history of the
Universe—scales not accessible to current or planned particle physics
experiments. The 3G network will probe those energy scales with its excellent
sensitivity to stochastic backgrounds.

###  4.1 Standard Siren Cosmology

Hubble Constant: GWs from a compact binary merger support a direct measurement
of the source’s luminosity distance. Combined with the redshift obtained from
the EM counterpart, or with galaxy catalogs, this gives an estimate the
present value of the Hubble parameter $H_{0}$ [208, 8]. It is estimated that
about ten mergers with EM counterparts would be required to reach an accuracy
of 5% and 200 to reach 1% [221, 222, 223]. While binary NS events are
promising based on GW170817, NS-BH and BH-BH mergers due to precession of the
orbital plane induced by spin-orbit coupling [224] or the presence of higher
multipole modes in the observed waveform [225, 226], can break the degeneracy
between the orbital inclination and luminosity distance, and provide more
accurate distance measurements. EM observations could also break this
degeneracy [227]. There is significant potential in statistical methods as
well, where binary mergers without EM counterparts are combined with galaxy
catalogs to make inferences [228]. For example, 3G detectors could localize
some sources within a volume where on average only one galaxy is present [164,
229, 226], although the method is limited by the peculiar velocity at the
redshift of interest and the distance uncertainty $\sim 1\%$ from GW
observations.

Precision Cosmology: GWs offer a new approach to probing the dark energy
properties either by using redshift measurements from EM counterparts, or by
using statistical methods [230, 231, 232, 233, 234, 235, 236, 237, 238]. The
3G network will measure standard sirens out to large redshifts, $z\,\sim 10$,
significantly farther than what is possible with the standard candles. Being
susceptible to a completely different set of systematic errors from those due
to type Ia supernovae this approach will provide a complementary probe
precision cosmology and of comparable sensitivity to those due to the cosmic
microwave background, baryon acoustic oscillation, and supernovae. An example
is shown in Figure 4.1 (left) [237, 238], where addition of standard sirens
improves the accuracy of the measured dark energy equation of state parameter
$w_{0}$.

Measuring Cosmological Parameters and Testing Modified Gravity Theories

Figure 4.1: Left: $1\sigma$ and $2\sigma$ contours of the two-dimensional
likelihood in the plane of the matter energy density $\Omega_{\mathrm{M}}$ and
the dark energy equation of state parameter $w_{0}$, with the combined
contribution from Planck CMB data + baryon acoustic oscillations (BAO) +
supernovae (red), the contribution from $10^{3}$ standard sirens at Einstein
Telescope (gray), and the total combined result (blue). Right: two-dimensional
likelihood in the $(\Xi_{0},w_{0})$ plane is shown, where $\Xi_{0}$ captures
the deviation between the GW and EM luminosity distances. The mock catalog of
standard sirens is generated assuming $\Lambda$CDM as the fiducial model
($w_{0}=-1$ and $\Xi_{0}=1$) and the plot shows the accuracy in the
reconstruction of $w_{0}$ and $\Xi_{0}$ (plot from [238]).

Modified Gravity Theories: Standard sirens are sensitive to another powerful
signature of the dark energy sector that is not accessible to EM observations.
A generic modified gravity theory induces modifications, with respect to the
standard model of cosmology, in the cosmological background evolution and
perturbations. Indeed, theories with extra dimensions [239], some scalar-
tensor theories [240, 241, 242, 243, 244], as well as a nonlocal modification
of gravity [245, 246, 247, 237, 238], are characterized by GWs propagating at
the speed of light but with their amplitude decreasing differently with the
scale factor than in GR. Consequently, the standard sirens would measure a
different luminosity distance compared to their EM counterparts. The 3G
network will be sufficiently sensitive to search for this deviation, and probe
multiple classes of modified theories of gravity in the context of their dark
energy content (Figure 4.1, right) [237, 238].

###  4.2 Early History of the Universe

Stochastic GW backgrounds could either be astrophysical in origin, generated
by a myriad of individual sources, or it could be generated by quantum
processes associated with inflation and spontaneous symmetry phase transitions
breaking in the early Universe. Figure 4.2 shows examples of GW energy density
spectra for some of the cosmological background models in comparison with the
best current upper limits and future expected detector sensitivities.
Cosmological background is arguably the most fundamentally impactful
observation that GW observatories could make. The astrophysical background,
however, may mask the primordial background over much of the accessible
spectrum, while still carrying important information about the evolution of
structure in the Universe. Techniques are being developed to identify and
estimate these various contributions to the stochastic GW background [248].

Stochastic Background Sources and Detector Sensitivities

Figure 4.2: Stochastic GW background for several proposed model spectra in
comparison with past measurements (Advanced LIGO upper limit [249],
constraints based on the big bang nucleosynthesis and cosmic microwave
background (CMB) observations, low-$l$ CMB observations, and pulsar timing
[250]), and future expected sensitivities [251], (the final sensitivity of
Advanced LIGO [252], Cosmic Explorer [90], and LISA, all assuming 1 year of
exposure [253, 254]). The gray band denotes the expected amplitude of the
background due to the cosmic population of compact binary mergers, based on
the observed coalescieng binary systems [255].

Irreducible GW background from inflation: Inflation represents the leading
framework to explain the properties and initial conditions of the observed
Universe. During inflation massless fields experience quantum fluctuations,
and due to the accelerated expansion small fluctuations with wavelengths
initially smaller than the Hubble radius are amplified and stretched to super-
Hubble scales. This applies, in particular, to tensor perturbations [210, 211,
212] that re-enter the Hubble radius after inflation and turn into a
stochastic GW background. In the standard slow-roll inflationary model (shown
in Figure 4.2), the energy density spectrum of this background is likely below
the proposed sensitivity of the 3G network, although upgrades to 3G detectors
could be sufficiently sensitive to observe this background.

Beyond the irreducible background from inflation: Additional processes during
or immediately after inflation could lead to significant amplification of the
stochastic background in the frequency band of 3G detectors. For example,
coupling of axions to the scalar field of inflation could extend GW production
with significant enhancement at higher frequencies [256, 257] as shown in Fig.
4.2. Furthermore, the resulting background is distinctly chiral (i.e. only one
polarization is excited) and non-Gaussian [258], unique predictions which can
be used to differentiate it unambiguously from other GW backgrounds. Similar
trends in the background spectrum are also possible if inflation is followed
by a phase with a stiff equation of state ($w>1/3$), that could be detectable
with 3G detectors [259, 213, 214, 215].

First order phase transitions: Following the end of inflation, the Universe
has undergone quantum chromodynamic, electroweak, and, possibly, other phase
transitions. Currently, an experimentally verified physical model lacks energy
scales higher than the electroweak scale. Several proposed extensions of the
Standard Model predict the occurrence of phase transitions. Any experimental
confirmation that such phase transitions took place in the early Universe
would constitute a step change in our understanding of particle theory at
energy scales inaccessible to terrestrial experiments.

To be an efficient direct source of GWs, a phase transition must be of first
order. First-order phase transitions proceed through the nucleation of bubbles
of the, energetically more favourable, true vacuum in the space-filling false
vacuum. The dynamics of the bubble expansion and collision is
phenomenologically rich, and the sources of GWs are the tensor anisotropic
stresses generated by these multiple phenomena: the bubble wall’s expansion
[217, 260], the sound waves in the plasma [219], and the subsequent
magnetohydrodynamic turbulence [261, 220]. The nature of the phase transition
and its energy scale determine the amplitude and the spectral shape of the GW
background. An example of such a background is shown in Figure 4.2 which is
potentially within reach of the 3G network [254].

Cosmic Strings: Topological defects such as cosmic strings may arise in the
aftermath of a phase transition [262]. Often, the string tension is the only
free parameter and it defines the energy scale of the phase transition and the
accompanying spontaneous symmetry breaking scale that leads to the formation
of cosmic strings. It is also possible to form a network of fundamental cosmic
(super)strings. Cosmic strings predominantly decay by the formation of loops
and the subsequent GW emission by cosmic string cusps and kinks [263, 264].
Searches for individual bursts of GWs from cosmic strings and for the
stochastic background from a string network have placed a strong constraint on
the string tension for the three well-known models [265, 266, 267, 268]. The
3G network will either detect cosmic strings or improve on these bounds by
eight orders of magnitude, depending on the model (see Fig. 4.2).

Dark Photons: A dark photon is proposed to be a light but massive gauge boson
in an extension of the Standard Model. If sufficiently light, the local
occupation number of the dark photon could be much larger than one, so it can
then be treated as a coherently oscillating background field that imposes an
oscillating force on objects that carry dark charge. The oscillation frequency
is determined by the mass of the dark photon. Such effects could result in a
stochastic background that could be measured by 3G detectors, potentially
exploring large parts of the parameter space of such models [269].

###  4.3 Astrophysical Binary Foregrounds and Large Scale Structure

The cosmological population of compact binary mergers will give rise to a
stochastic foreground of GWs [270, 271, 272, 273, 274, 275]. The amplitude of
this foreground is estimated to be $\Omega_{\text{GW}}\sim 10^{-9}$ at 25 Hz,
and is likely to be detected by Advanced LIGO and Advanced Virgo [209]. The 3G
network, thanks to better low-frequency sensitivity, will probe
$\Omega_{\text{GW}}\sim 10^{-13}$–$10^{-12}$ [276, 277, 270]. The 3G network
could, therefore, detect the predicted spatial anisotropy [278, 279] and non-
gaussianity [279] in the energy density of this foreground. In particular,
measurements of higher order correlation functions would be extremely useful
in understanding the large scale structure of the Universe.

Figure 4.2 shows that the amplitude of this foreground is several orders of
magnitude stronger than most cosmological GW backgrounds, hence masking the
cosmological signals discussed above. However, a large fraction of the binary
merger signals will be individually detected by the 3G network, allowing for
the possibility to subtract this foreground to probe a cosmic background of
$\Omega_{\rm GW}\sim 10^{-13}$ [277, 270, 248]. Small errors in subtraction
could lead to a substantial residual foreground—novel methods are being
explored to enable more effective subtraction [280].

Astrophysical sources other than compact binary mergers could also contribute
to the astrophysical GW foreground, including isolated NSs [281, 282, 283],
core collapse supernovae [284, 285] and population III binaries [286].
Distinguishing these unresolved foreground sources from the cosmological
background will require using spatial correlations (both GW-GW and GW-EM
correlations) and careful measurements of the foreground spectra. Studying the
properties of the astrophysical foreground will provide unique new information
on galactic and stellar physics and allow for new types of constraints on
astrophysical models.

###  4.4 Outlook for gravitational-wave cosmology and the early Universe

3G observatories will revolutionize our understanding of the evolution of the
Universe, from its earliest moments to the recent past. Measurements of the
frequency spectrum, spatial anisotropy, and polarization content of the
primordial stochastic GW background are likely to reveal imprints of the
physical laws and processes that drove the earliest phases of the Universe’s
evolution and take place at energy scales inaccessible to current or planned
particle physics experiments. Observation of the astrophysical, compact-binary
stochastic GW background and its properties would provide information on the
formation and evolution of matter in the Universe, going back to the time when
the first stars and galaxies were formed. More recent compact binary mergers
will be used as standard sirens to provide novel and independent measurements
of the expansion and acceleration of the late Universe, constraining the
fundamental nature of gravity and cosmological parameters. While the
irreducible inflationary stochastic GW background is likely not within reach
of the 3G network, it may be within reach of the follow-up upgrades, which
should be factored into the site selection and facility design of the 3G
detectors.

Science Requirements With 3G observatories we can investigate the fundamental
physics of the primeval Universe and probe its dark sectors: • a factor of
10-20 improvement beyond the sensitivity of advanced detectors is critical to
infer cosmological parameters at a precision that is competitive with current
measurements, • lowering the frequency response down to 5 Hz will allow the
observation of astrophysical foregrounds and their subtraction via better
estimation of source parameters, and • a factor of 10 improvement in strain
sensitivity (100 in energy density) over advanced detectors is required to
observe GW background from early Universe phase transitions.

##  Chapter 5 Extreme Gravity and Fundamental Physics

Science Target Explore new physics in gravity and in the fundamental
properties of compact objects

General Relativity (GR) is a mathematically elegant and physically appealing
theory that has been tremendously successful in explaining all relevant
astronomical observations and laboratory experiments[287, 288, 289].
Nonetheless, it is widely believed that GR is at best incomplete [289, 290],
representing an approximation to a more complete theory that cures some or all
of its deep conceptual problems. Black hole (BH) information loss, spacetime
singularities, cosmological constant and the lack of a viable formulation of
quantum gravity, have all added to the suspicion that GR violations will
eventually show up in observations [291, 292, 290, 293]. Over the past decade
new insights into the relationship between entanglement entropy and the
architecture of spacetime [294] on the one hand and the connection between
asymptotic symmetries, the BH entropy and infrared behaviour of quantum
gravity [295] on the other are all hinting towards a modified theory of
gravity. At the same time, the discovery of gravitational waves (GWs) has
provided a powerful new tool to test GR in a realm of the theory that is
inaccessible to other experiments and observations.

GW150914 was not only the first direct detection of GWs but also the first
ever observation of a binary black hole (BBH) [296]. Since then tens of BBH
mergers have been observed [297], GW190521 being the most massive system
discovered so far [128] that converted 9 solar masses to pure energy in a mere
100 ms. BBH mergers are arguably the most powerful phenomena in nature, save
for the Big Bang, the signals coming from a region where both the spacetime
curvature and gravitational field are extremely large. They have helped test
Einstein’s gravity in regimes where the theory has never been tested before
[80]. 3G observatories will make a step change in studying gravity and the
nature of ultra-compact objects.

Key Science Goals The 3G GW observatories will enable unprecedented and unique
science in _extreme gravity_ and _fundamental physics_ : • The nature of
gravity: Are the building-block principles and symmetries in nature, e.g.
Lorentz invariance and equivalence principle, invoked in the description of
gravity valid at all scales? • The nature of compact objects: Are black holes
and neutron stars the only ultra-compact objects in the Universe? If other
compact objects exist what are their signatures in gravitational waves? • The
nature of dark matter: Is dark matter composed of particles or dark objects or
is it a manifestation of failure of general relativity?

GWs are copiously produced in regions of strong gravity and relativistic
motion. Yet the waves carry pristine information about their sources because
they interact feebly with matter and remain unscathed as they propagate over
billions of light years to Earth. This makes them ideal for testing GR in new
ways that could reveal subtle departures from the theory [298, 299, 77, 170].
We can now directly probe the two-body dynamics (specifically, the complex
orbital motion predicted in GR such as precessional effects), the spacetime
structure near BHs and the dynamics of their horizons, and if the Universe
depicted by electromagnetic (EM) and particle messengers is the same as the
one revealed by GWs. In addition, imprint in the observed GWs are the
signatures of compact objects that can be deformed in a way that BHs cannot
be. This should help us detect a new class of ultra-compact compact objects
consisting of boson condensates or other exotic particles and fields should
they exist. Finally, the presence of dark matter around compact binaries or
their accumulation in neutron star (NS) cores, will also modify the observed
signals. Hence, GWs could be used to measure the properties of dark matter
particles—their masses and interaction cross sections with hadronic matter.

###  5.1 Nature of Gravity.

Probing the nature of gravity and its possible implications on fundamental
physics is a high-reward, even if uncertain, prospect of GW observations. To
our knowledge, astrophysical BHs and relativistic stars exhibit the largest
curvature of spacetime accessible to us. They are, therefore, ideal systems to
observe the behaviour of spacetimes under the most extreme gravitational
conditions. New physics indicative of departures from the basic tenants of GR
could reveal itself in high fidelity waveforms expected to be observed in the
3G network. Such signals would provide a unique access to extremely warped
spacetimes and gain invaluable insights into GR or what might replace it as
the theory of gravity.

Figure 5.1 provides a perspective of the reach of different
missions/facilities and their target regime with respect to characteristic
spacetime curvature ($R$) and gravitational potential $\Phi$ (which for binary
systems can be equated with $v^{2}/c^{2}$, where $v$ is the characteristic
velocity of companion stars and $c$ the speed of light).

Probing Gravity at all Scales Figure 5.1: Illustration of the reach in
curvature scales vs potential scales targeted by different, representative,
past/current/future missions. In this figure, $M$ and $L$ are the
characteristic mass and length involved in the observable associated to each
mission. For instance, in observables associated to binary systems $M$ is the
total mass and $L$ the binary’s separation, in this case $M/L$ is related to
$v^{2}/c^{2}$ through the virial theorem.

To this end, beyond having access to the sensitivity and frequency windows of
3G detectors, guidance from theory, together with further refinements in data
analysis, will be of utmost importance to harness this potentially
revolutionary opportunity. On the theoretical front a major challenge in
extracting new physics with GWs is that, in principle, one needs to model the
characteristics of the emitted signal for the desired physical scenarios
beyond the framework of GR and then confront it with the data [300, 301]. The
powerful perspective of effective field theory [302, 303, 304, 305]) allows
one to build extensions to GR with higher-order corrections and search for new
physics, even before a new fundamental theory and its low-energy phenomenology
is fully developed (see, e.g., Refs. [306, 307, 308]). Among possible
departures under scrutiny are the following:

New fields, particles and polarizations: GR has not only passed every
experimental and observational test that it has been subject to but it is also
a very robust theory. In fact, any physically meaningful departures from GR
necessarily require the presence of extra degrees of freedom, e.g. scalar and
vector fields, in addition to the metric tensor [309]. Such additional degrees
of freedom also generically arise in the low-energy limit of quantum gravity
theories, which often lead to violations of the strong equivalence principle.
Among possible theories, those with an additional scalar field, e.g. the
Brans-Dicke theory, are relatively simple [310, 311]. Yet they could give rise
to exciting new phenomenology in strong gravitational fields indicative of
failure of GR [312, 313]. Such theories, therefore, serve as excellent proxies
of the type of new physics we can hope to discover. Additionally, if a
binary’s companions can become dressed with a scalar configuration [314, 315,
316, 317], we can expect the emission of scalar GWs, in addition to tensorial
ones, with the dominant component being dipolar emission [300]. Such emissions
lead to additional polarizations, beyond the two in GR, that could be detected
directly with a network of detectors [76, 318] or indirectly inferred from
their effects on the source’s dynamics and consequent impact on the observed
GWs [300].

Graviton mass and speed of GWs: Recently, the possibility that gravitons could
have mass has resurfaced in theoretical physics within extensions of GR [319,
320]. In a massive graviton theory GWs would be dispersed as they propagate
from their sources to Earth, causing a change in the phase evolution of the
observed signal relative to GR. The current best bound on the graviton mass
$m_{g}$ comes from modifying the GR dispersion relation for GWs and this sets
the bound $m_{g}<5.0\times 10^{-23}\,{\rm eV}/c^{2}$ [80]. The 3G network
could improve this bound by two orders-of-magnitude by detecting sources from
as far as $z\sim 50$ and further constrain massive graviton theories.

Lorentz invariance and parity violations: Lorentz invariance is regarded as a
fundamental property of the Standard Model of particle physics, tested to a
spectacular accuracy in particle experiments [321]. In the gravitational
sector, constraints are far less refined. Theories with Lorentz invariance
violation (e.g., Hořava–Lifschitz [322] and Einstein-æther [323]) give rise to
significant departures from GR on the properties of BHs [324, 325], existence
of additional polarizations [326], and the propagation of GWs through
dispersion and birefringence [327, 78]. Furthermore, parity violations in
gravity arise naturally within some flavors of string theory [328], loop
quantum gravity [329] and inflationary models [304]. The associated
phenomenologies are, to some degree, understood from effective theories [330].
For instance, they give rise to BHs with nontrivial pseudo-scalar
configurations that violate spatial parity [331]. The resulting scalar dipole
leads to a correction to the GWs produced in a binary inspiral and merger
signal [332, 333, 334]. Additionally, parity violating theories can exhibit
birefringence, thus impacting the characteristics of GWs tied to their
handedness [335]. All of these effects will be greatly constrained by the 3G
network as it will observe sources at redshifts of $z\sim 50$ and higher [335]
and will have the ability to measure additional polarizations.

Ultra-light Bosonic Clouds: Ultralight bosons have been proposed in various
extensions of the Standard Model [336]. When the Compton wavelength of
ultralight bosons (masses in the range $10^{-21}$ eV–$10^{-11}$ eV) is
comparable to the horizon size of a spinning stellar-mass or supermassive BH,
superradiance can cause BH spin to decay, populating bound Bohr orbits around
the BH, with an exponentially large number of particles [337, 338, 339]. Such
bound states, in effect gravitational atoms, have bosonic clouds with masses
up to $\sim$ 10% of the BH mass [340, 341, 342]. Once formed, the clouds
annihilate over a longer timescale through the emission of coherent, nearly-
monochromatic, GWs [340, 343].

Presence of such clouds could be detected via blind searches in the Milky Way
[343, 344, 345, 346, 347] or directed searches aimed at a candidate BH, such
as that formed in a merger event [343, 344, 348, 345, 349], or observations of
a stochastic background from an unresolved population [346, 347]. Annihilation
of such clouds can also impact a binary’s dynamics and thus the GWs produced
during the inspiral [350]. Such a modified GW signal is a promising target for
3G detectors with a few to hundreds of events per year expected for bosons in
the $\sim 10^{-13}$–$10^{-12}$ eV range [344]. Measuring the spin and mass
distribution of merging BBHs can provide evidence for characteristic BH
spindown from superradiance [344, 345], which would allow exploration of a new
parameter space for ultralight bosons [163]. In addition, the presence of such
clouds can be probed through the imprint of finite-size effects on the compact
objects in a binary system [350]. Some dark-matter candidates alternative to
weakly interacting massive particles (e.g., fuzzy dark matter [351], axion-
like particles, and other ultralight bosons [336]) predict exotic compact
objects (or ECOs) either in the form of boson stars or in the form of
condensates that form spontaneously due to BH superradiant instabilities.

Large, non-local, quantum effects: Semi-classical arguments have been put
forward to support the possibility of exotic states of matter or dressed
compact objects with further structure stemming from quantum gravitational
origin. Examples of electromagnetically dark but horizonless compact objects
include fuzzballs [352, 353], gravastars [354], dark stars [355, 356], and
others [357, 358]. Additionally, new non-local physics at the horizon scale
has been suggested by firewall arguments [359] as well as other quantum
effects [360, 361, 362, 363]. These scenarios can generically give rise to
signatures that can potentially be detected by the 3G network. Thus, GWs
facilitate a unique window to these arguably speculative ideas, with far
reaching consequences if observed.

###  5.2 Nature of Compact Objects.

Observational evidence so far suggests that compact massive objects in the
Universe exist in the form of BHs and NSs. Binary systems composed of such
objects provide ideal scenarios to unravel both astrophysical and fundamental
physics puzzles such as elucidating the connections of strong gravity with the
most energetic phenomena in our Universe, exploring the final state conjecture
[364] (namely, the end point of gravitational collapse is a Kerr BH), and
probing the existence of horizons.

Nature of black holes: Kerr BHs are characterized by just two parameters,
their mass and spin angular momentum. This remarkable property implies that
the oscillations of a perturbed BH are rather unique. Indeed, a perturbed BH
returns to its quiescent state by losing the energy in its deformation into
GWs. The emitted waves consist of a spectrum of damped sinusoids called quasi-
normal modes whose frequencies and decay times are determined by the BH’s mass
and spin.

Test of Black Hole Nature Figure 5.2: Projections of the $95\%$ confidence
intervals for the fundamental quasi-normal mode frequency $f_{22},$ the
corresponding damping time $\tau_{22}$ and a sub-dominant mode $f_{33})$, as
function of the mass ($M$) and dimensionless spin ($j\equiv J/M^{2}$) of the
final compact object for a _single_ GW150914-like event with advanced
detectors at design sensitivity (HLV, dashed lines) and the 3G network (solid
lines). The yellow star corresponds to the true value of the BH’s mass and
spin used in the simulation.

These parameters of the BH can be inferred from the measurement of a single
mode frequency and its decay time. Detection of several modes would facilitate
multiple null tests of the Kerr nature of BHs [365, 168, 366, 367, 368, 369,
370, 371]. Such tests look for consistency in the masses and spins inferred
from the different modes (see Fig. 5.2). The sensitivity of a 3G network is
necessary for the precision with which such consistency tests can be carried
out. Multiple loud events expected to be detected by the 3G network will
provide exquisite tests of the Kerr nature of compact objects.

Beyond black holes: From a phenomenological standpoint, BHs and NSs are just
two species of a larger family of compact objects. More exotic species are
theoretically predicted in extensions to GR, but also in particular scenarios
within GR [363, 372]. For instance, extremely compact objects (ECOs) arise
from beyond-standard model fundamental fields minimally coupled to gravity
(e.g., boson stars [373]), in Grand Unified Theories in the early Universe
(e.g., cosmic strings [262]), from exotic states of matter, as dressed compact
objects with further structure stemming from quantum gravitational origin
[360, 362] or new physics at the horizon scale (e.g., firewalls [359]), or as
horizonless compact objects in a variety of scenarios, for example, fuzzballs,
gravastars, and dark stars [352, 354, 355, 356, 357, 358]. GW observations
provide a unique discovery opportunity in this context, since exotic matter
might not interact electromagnetically or any EM signal from the surface of an
ECO might be highly redshifted [363]. Example GW signatures from the inspiral
epoch include dipole radiation as well as a variety of matter effects as in
the case of NSs [372].

An ECO could be parameterized by the gravitational redshift $z_{g}$ near its
surface. This parameter can change by several orders of magnitude depending on
the model. BHs have $z_{g}\rightarrow\infty$ while NSs and the most compact
theoretically constructed boson stars have $z_{g}\sim{\cal O}(1)$. For
sufficiently large values of $z_{g}$ compact objects could behave like BHs
with increasing precision. Studies of the geodesic motion and quasi-normal
modes indicate that ECOs with $z_{g}\lesssim 1.4$ display internal structure
effects that can be discerned in future GW observations. For larger values of
$z_{g},$ ECOs mimic BHs [374, 363, 375] as departures are redshifted to ever
smaller values. Interestingly, models of near-horizon quantum
structures—motivated by various scenarios [352, 353, 354, 359]—can reach
redshifts as high as $z_{g}\sim{\cal O}(10^{20})$ for ECOs in the frequency
band of ground-based detectors. GWs could be our only hope to detect or rule
them out.

Additionally, while the ringdown signal that follows from the merger of a
compact binary can be qualitatively similar to that of a BH, quasi-normal
modes of, e.g., gravastars, axion stars and boson stars, are different from
Kerr BHs [170]. In addition to gravitational modes, matter modes might be
excited in the ringdown of an ECO, akin to the fluid modes excited in a
remnant NS [372]. In the case of certain BH mimickers the prompt ringdown
signal is identical to that of a BH. However, these objects generically
support quasi-bound trapped modes which produce a modulated train of pulses at
late time. These modes appear after a delay time whose characteristics are key
to test Planckian corrections at the horizon scale. The 3G network will have
unprecedented ability extract all these modes and explore the existence of
ECOs [363].

###  5.3 Nature of Dark Matter.

The exquisite ability of 3G detectors to probe the population and dynamics of
electromagnetically dark objects throughout the Universe and harness deep
insights on gravity can help reveal the nature of dark matter and answer key
questions about its origin.

Black holes as dark matter candidates: LIGO and Virgo discoveries have revived
interest in the possibility that dark matter could be composed, in part, of
primordial black holes (PBHs) of masses $\sim 0.1$–$100\,M_{\odot}$ [376, 377,
378]. Such BHs might have formed from the collapse of large primordial density
fluctuations in the very early Universe or during inflation [379, 103]. The
exact distribution of their masses and spins depends on the model of
inflation, which might be further affected by processes in the early Universe
such as the quantum chromodynamics phase transition (QCD) [380, 294].
Detection of binaries composed of objects much lighter than stellar-mass BHs
or mass and spin distributions showing an excess in a certain range, could
point towards the existence of PBHs [381]. Identifying mergers at redshifts
$z>30,$ when first stars were yet to form, would be another hint towards this
formation channel [382]. With the sensitivity to observe mergers at redshifts
as large as $z\sim 50,$ the 3G network will be uniquely positioned to
determine the mass, spin and redshift distributions of BHs, which will be
crucial to test the hypothesis that dark matter consists of PBHs [383]. Figure
5.3 shows the current bounds and discovery potential of 3G detectors.

Detection of dark matter with compact objects: Apart from probing whether dark
matter can be partially made up of PBHs, GWs can also scrutinize models where
dark matter consists of particles beyond the Standard Model, e.g., weakly
interacting massive particles [384], fuzzy dark matter [351] or axion-like
particles [336]. Indeed, BBHs evolving in a dark-matter rich environment will
not only accrete the surrounding material, but also exert a gravitational drag
on the dark matter medium, which affects their orbital dynamics [385, 386,
387]. Even though their magnitude is small, drag and accretion could have a
cumulative effect over a large number of orbits that could be detected by a
combination of observatories in space and 3G detectors [372].

Primordial Black Holes as Dark Matter Figure 5.3: PBHs as dark matter: The
plot shows upper limits based on the observation of microlensing of stars
[388, 389], microlensing of supernovae (SNe) [390], caustic disruption [391,
392, 393], distortions in the cosmic microwave background by Planck [394, 395]
and the stability of Eridanus II dwarf galaxy [396, 397]. GW constraints
correspond to LIGO searches for sub-solar compact objects [381] and stellar-
mass mergers [398]. The shaded regions correspond to the mass function
imprinted by the QCD phase transition for different PBH abundances and a
primordial scale invariant spectrum [380]. 3G detectors can improve the
current bounds by many orders of magnitude.

Additionally, dark matter that interacts with standard model particles can
scatter, lose energy, and be captured in astrophysical objects [399, 400, 401,
402]. The dark matter eventually thermalizes with the star, and accumulates
inside a finite-size core. The presence of dark matter would change the core’s
equation of state imprinting its signature into GWs emitted during the
inspiral and merger of such objects in a binary system [403]. In certain
models, asymmetric dark matter can accumulate and collapse to a BH in the
dense interiors of NSs. The core can grow by accumulating the remaining NS
material, in effect turning NSs into light BHs in regions of high dark-matter
density such as galactic centers [404, 405]. This provides a mechanism for
creating light BHs that could be observed by 3G detectors. However, BHs that
result from implosion of dark matter accreting NSs will always be heavier than
$\sim 1\,M_{\odot},$ any BH candidates of mass $\lesssim 1\,M_{\odot}$ could
only be primordial in origin.

###  5.4 Outlook on Exploring Extreme Gravity and Fundamental Physics

Einstein’s description of gravity led to a revolution in our thinking of the
very nature of spacetime itself. Gravity is the manifestation of the curvature
of spacetime caused by matter and energy density. GR has so far passed every
test to which it has been subject to, yet some of its predictions are deeply
troubling. The physical singularity at the Big Bang, loss of information when
matter and energy fall into a BH are but examples of predicaments faced by the
theory for which no satisfactory resolutions exist. Moreover, observations are
hinting that our knowledge of the constituents of the Universe is
underwhelmingly poor and breakthroughs in the detection of new particles and
fields is keenly awaited.

Science Requirements GW observations by the 3G network could provide answers
to some of the most fundamental questions about spacetime and matter. The
capabilities required to answer them are: • high fidelity observations
(SNR>1000) of a large number of sources to discover rare events that carry
unique signatures of new particles and fields, dark matter and violations of
GR, • a network of at least one ET and two CEs to constrain or detect
additional polarizations, • access to frequencies below the sensitivity of
current detectors to track GWs over a much longer period to test GR
predictions and to detect dipole radiation, and • ability to identify black
holes at large redshifts $z\geq 50$ to detect birefringence, improve bounds on
graviton mass and discover primordial black holes.

##  Chapter 6 Sources at the Frontier of Observations

Science Target Understand physical processes that underlie the most powerful
astrophysical phenomena.

In addition to revealing dark astrophysical processes, gravitational waves
(GWs) also offer a new window into extreme phenomena inside compact
astronomical sources. While electromagnetic (EM) observations reveal the
conditions in the surface regions, GWs encode information about the internal
dynamics of these systems, particularly the way the distribution of matter is
changing. This will allow us to address longstanding mysteries about the
underlying physical mechanisms that power nature’s most extreme phenomena. For
example, GWs emitted along with light and neutrinos during the aftermath of
the collapse of a massive star’s core will yield unique insight into why the
exterior of the star explodes as a supernova and the nature of the remnant
that it leaves behind. GWs from magnetar flares or glitching radio pulsars
will elucidate the physical mechanism that causes these bursts of light and
provide an unprecedented glimpse deep into the interior of neutron stars
(NSs). GWs produced by spinning NSs will allow us to study the structure of
ultra-dense NS matter and test particle physics theories in extreme conditions
of strong gravity. Sensing these sources of GWs with a network of 3G detectors
in concert with EM observatories and neutrino detectors will allow us to learn
new physics that is otherwise inaccessible.

Key Science Goals Observations with the 3G network, further enhanced with EM
and neutrino observatories, will allow us to probe new extreme environments
and answer key questions about exotic astrophysical transients: • GWs from
core-collapse supernovae. How do massive stars explode to form NSs and black
holes? What are the physical processes involved and how can they be harnessed
to advance our understanding of dense matter, neutrinos, and dark matter? •