contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
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# Snowmass2021 CMB-HD White Paper

The CMB-HD Collaboration  http://cmb-hd.org  Simone Aiola  Center for
Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY
10010 USA  Yashar Akrami  CERCA/ISO, Department of Physics, Case Western
Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA  Department
of Physics, Imperial College London, Blackett Laboratory, Prince Consort Road,
London SW7 2AZ, United Kingdom  Laboratoire de Physique de l’École Normale
Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, F-75005 Paris,
France  Observatoire de Paris, Université PSL, Sorbonne Université, LERMA, 750
Paris, France  Kaustuv Basu  Argelander Institute for Astronomy, University of
Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany  Michael Boylan-Kolchin
Department of Astronomy, The University of Texas at Austin, 2515 Speedway,
Stop C1400, Austin, Texas 78712, USA  Thejs Brinckmann  Dipartimento di Fisica
e Scienze della Terra, Universitá degli Studi di Ferrara, via Giuseppe Saragat
1, 44122 Ferrara, Italy  Istituto Nazionale di Fisica Nucleare (INFN), Sezione
di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy  Sean Bryan  School
of Earth and Space Exploration, Arizona State University, 781 Terrace Mall,
Tempe, AZ 85287, USA  Caitlin M Casey  Department of Astronomy, The University
of Texas at Austin, 2515 Speedway, Stop C1400, Austin, Texas 78712, USA  Jens
Chluba  Jodrell Bank Centre for Astrophysics, Alan Turing Building, University
of Manchester, Manchester M13 9PL, United Kingdom  Sébastien Clesse  Service
de Physique Théorique (CP225), Université Libre de Bruxelles, Boulevard du
Triomphe, 1050 Brussels, Belgium  Francis-Yan Cyr-Racine  Department of
Physics and Astronomy, University of New Mexico, 210 Yale Blvd NE,
Albuquerque, NM 87106, USA  Luca Di Mascolo  Astronomy Unit, Department of
Physics, University of Trieste, via Tiepolo 11, Trieste 34131, Italy  INAF -
Osservatorio Astronomico di Trieste, via Tiepolo 11, Trieste 34131, Italy
IFPU - Institute for Fundamental Physics of the Universe, Via Beirut 2, 340
Trieste, Italy  Simon Dicker  Department of Physics and Astronomy, University
of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA  Thomas
Essinger-Hileman  NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
Gerrit S. Farren  Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, Cambridge CB3 0WA, United Kingdom  Department of
Physics and Astronomy, Haverford College, 370 Lancaster Avenue, Haverford,
Pennsylvania 19041, USA  Michael A. Fedderke  The William H. Miller III
Department of Physics and Astronomy, The Johns Hopkins University, Baltimore,
MD 21218, USA  Simone Ferraro  Lawrence Berkeley National Laboratory, One
Cyclotron Road, Berkeley, CA 94720, USA  Berkeley Center for Cosmological
Physics, Department of Physics, University of California, Berkeley, CA 94720,
USA  George M. Fuller  Center for Astrophysics and Space Sciences, University
of California, San Diego, La Jolla, CA 92093, USA  Nicholas Galitzki
University of California, San Diego, Department of Physics, San Diego, CA
92093, USA  Vera Gluscevic  Department of Physics and Astronomy, University of
Southern California, Los Angeles, CA, 90007, USA  Daniel Grin  Department of
Physics and Astronomy, Haverford College, 370 Lancaster Avenue, Haverford,
Pennsylvania 19041, USA  Dongwon Han  Department of Applied Mathematics and
Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United
Kingdom  Matthew Hasselfield  Center for Computational Astrophysics, Flatiron
Institute, 162 5th Avenue, New York, NY 10010 USA  Renée Hložek  Dunlap
Institute for Astronomy and Astrophysics, University of Toronto, 50 St George
Street, Toronto, Ontario, M5S 3H4, Canada  David A. Dunlap Department of
Astronomy and Astrophysics, University of Toronto, 50 St George Street,
Toronto, Ontario, M5S 3H4, Canada  Gil Holder  University of Illinois at
Urbana-Champaign, 1110 W Green, Urbana IL 61801, USA  Selim C. Hotinli  The
William H. Miller III Department of Physics and Astronomy, The Johns Hopkins
University, Baltimore, MD 21218, USA  Bhuvnesh Jain  Department of Physics and
Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA
19104, USA  Bradley Johnson  Department of Astronomy, University of Virginia,
Charlottesville, VA 22904, USA  Matthew Johnson  Department of Physics and
Astronomy, York University, Toronto, ON M3J 1P3, Canada  Perimeter Institute
for Theoretical Physics, 31 Caroline St N, Waterloo, ON N2L 2Y5, Canada
Pamela Klaassen  UK Astronomy Technology Centre, Blackford Hill, Edinburgh EH9
3HJ, United Kingdom  Amanda MacInnis  Physics and Astronomy Department, Stony
Brook University, Stony Brook, NY 11794, USA  Mathew Madhavacheril  Perimeter
Institute for Theoretical Physics, 31 Caroline St N, Waterloo, ON N2L 2Y5,
Canada  Department of Physics and Astronomy, University of Southern
California, Los Angeles, CA, 90007, USA  Sayan Mandal  Physics and Astronomy
Department, Stony Brook University, Stony Brook, NY 11794, USA  Philip
Mauskopf  School of Physics and Astronomy, Cardiff University, Queen’s
Buildings, The Parade, Cardiff, CF24 3AA, United Kingdom  School of Earth and
Space Exploration and Department of Physics, Arizona State University, Tempe,
AZ 85287, USA  Daan Meerburg  Van Swinderen Institute for Particle Physics and
Gravity, University of Groningen, Nijen- borgh 4, 9747 AG Groningen, The
Netherlands  Joel Meyers  Department of Physics, Southern Methodist
University, 3215 Daniel Ave, Dallas, TX 75275, USA  Vivian Miranda  Physics
and Astronomy Department, Stony Brook University, Stony Brook, NY 11794, USA
Tony Mroczkowski  European Southern Observatory (ESO), Karl- Schwarzschild-
Strasse 2, Garching 85748, Germany  Suvodip Mukherjee  Perimeter Institute for
Theoretical Physics, 31 Caroline St N, Waterloo, ON N2L 2Y5, Canada
Gravitation Astroparticle Physics Amsterdam (GRAPPA), Anton Pannekoek
Institute for Astronomy and Institute for Physics, University of Amsterdam,
Science Park 904, 1090 GL Amsterdam, The Netherlands  Institute Lorentz,
Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands  Delta
Institute for Theoretical Physics, Science Park 904, 1090 GL Amsterdam, The
Netherlands  Moritz Münchmeyer  Department of Physics, University of
Wisconsin-Madison, Madison, WI 53706, USA  Julian Munoz  Harvard-Smithsonian
Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA  Sigurd Naess
Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New
York, NY 10010 USA  Daisuke Nagai  Department of Physics, Yale University,
P.O. Box 208120, New Haven, CT, 06520, USA  Toshiya Namikawa  Kavli Institute
for the Physics and Mathematics of the Universe (WPI), UTIAS, The University
of Tokyo, Kashiwa, Chiba 277-8583, Japan  Laura Newburgh  Department of
Physics, Yale University, P.O. Box 208120, New Haven, CT, 06520, USA  Hồ Nam
Nguyễn Department of Physics, University of California, Berkeley, CA 94720,
USA  Michael Niemack  Cornell University Physics Department and Astronomy
Department, Ithaca, NY 853 USA  Benjamin D. Oppenheimer  CASA, Department of
Astrophysical and Planetary Sciences, University of Colorado, 389 UCB,
Boulder, CO 80309, USA  Harvard-Smithsonian Center for Astrophysics, 60 Garden
St., Cambridge, MA 02138, USA  Elena Pierpaoli  Department of Physics and
Astronomy, University of Southern California, Los Angeles, CA, 90007, USA
Srinivasan Raghunathan  Center for AstroPhysical Surveys, National Center for
Supercomputing Applications, Urbana, IL 61801, USA  Emmanuel Schaan  Lawrence
Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA
Berkeley Center for Cosmological Physics, Department of Physics, University of
California, Berkeley, CA 94720, USA  Neelima Sehgal  Physics and Astronomy
Department, Stony Brook University, Stony Brook, NY 11794, USA  Blake Sherwin
Department of Applied Mathematics and Theoretical Physics, University of
Cambridge, Cambridge CB3 0WA, United Kingdom  Sara M. Simon  Fermi National
Accelerator Laboratory, MS209, P.O. Box 500, Batavia, IL, 60510, USA  Anže
Slosar  Physics Department, Brookhaven National Laboratory, Upton, NY 11973,
USA  Kendrick Smith  Perimeter Institute for Theoretical Physics, 31 Caroline
St N, Waterloo, ON N2L 2Y5, Canada  David Spergel  Center for Computational
Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010 USA  Eric
R. Switzer  NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
Pranjal Trivedi  Hamburger Sternwarte, University of Hamburg, Gojenbergsweg
112, D-21029 Hamburg, Germany  Yu-Dai Tsai  Department of Physics and
Astronomy, University of California, Irvine, CA 92697-4575, USA  Alexander van
Engelen  School of Earth and Space Exploration, Arizona State University, 781
Terrace Mall, Tempe, AZ 85287, USA  Benjamin D. Wandelt  Center for
Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY
10010 USA  Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de
Paris (IAP), 98 bis bd Arago, F-750 Paris, France  Sorbonne Université,
Institut Lagrange de Paris (ILP), 98 bis bd Arago, F-750 Paris, France  Edward
J. Wollack  NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA  Kimmy
Wu  Kavli Institute for Particle Astrophysics and Cosmology, Stanford
University, 452 Lomita Mall, Stanford, CA 94305, USA  SLAC National
Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA

###### Abstract

CMB-HD is a proposed millimeter-wave survey over half the sky that would be
ultra-deep (0.5 $\mu$K-arcmin) and have unprecedented resolution (15
arcseconds at 150 GHz). Such a survey would answer many outstanding questions
about the fundamental physics of the Universe. Major advances would be 1.) the
use of gravitational lensing of the primordial microwave background to map the
distribution of matter on small scales ($k\sim 10\leavevmode\nobreak\
h$Mpc-1), which probes dark matter particle properties. It will also allow 2.)
measurements of the thermal and kinetic Sunyaev-Zel’dovich effects on small
scales to map the gas density and velocity, another probe of cosmic structure.
In addition, CMB-HD would allow us to cross critical thresholds: 3.) ruling
out or detecting any new, light ($<0.1$ eV) particles that were in thermal
equilibrium with known particles in the early Universe, 4.) testing a wide
class of multi-field models that could explain an epoch of inflation in the
early Universe, and 5.) ruling out or detecting inflationary magnetic fields.
CMB-HD would also provide world-leading constraints on 6.) axion-like
particles, 7.) cosmic birefringence, 8.) the sum of the neutrino masses, and
9.) the dark energy equation of state. The CMB-HD survey would be delivered in
7.5 years of observing 20,000 square degrees of sky, using two new 30-meter-
class off-axis crossed Dragone telescopes to be located at Cerro Toco in the
Atacama Desert. Each telescope would field 800,000 detectors (200,000 pixels),
for a total of 1.6 million detectors.

##  1 Executive Summary

CMB-HD is an ambitious leap beyond previous and upcoming ground-based
millimeter-wave experiments. It will allow us to cross critical measurement
thresholds and definitively answer pressing questions in both astrophysics and
the fundamental physics of the Universe. The combination of CMB-HD with
contemporary ground and space-based experiments will also provide countless
powerful synergies.

Two critical advances uniquely enabled by CMB-HD are mapping over half the
sky: i) the distribution of all matter on small scales ($k\sim
10\leavevmode\nobreak\ h$Mpc-1) using the gravitational lensing of the cosmic
microwave background (CMB), and ii) the distribution of gas density and
velocity on small scales using the thermal and kinetic Sunyaev-Zel’dovich
effects (tSZ and kSZ). The combination of high-resolution and seven frequency
bands in the range of 30 to 350 GHz allows for separation of foregrounds from
the CMB. That plus the unprecedented depth of the survey over half the sky
allows CMB-HD to achieve the key science targets summarized in Table 1. This
white paper outlines the key science goals motivating the CMB-HD survey, as
well as the flowdown to measurement and instrument requirements. Additional
details are discussed in the Astro2020 Science White Paper [1], Astro2020 CMB-
HD APC [2], and Astro2020 CMB-HD RFI [3]. Further information can also be
found at https://cmb-hd.org.

Table 1: Summary of CMB-HD Key Science Goals

Science | Parameter | Sensitivity
---|---|---
Dark Matter & Dark Sectors |  |
Warm Dark Matter | $m_{\rm{WDM}}$ |  $m_{\rm{WDM}}<1$ keV with S/N $>5\sigma$
Fuzzy Dark Matter | $m_{\rm{FDM}}$ |  $m_{\rm{FDM}}<1\times 10^{-22}$ eV with S/N $>5\sigma$
Axion-Like Particlesa | $g_{a\gamma}$ |  $g_{a\gamma}<2.1\times 10^{-15}$ GeV${}^{-1}(m_{a}/10^{-22}\leavevmode\nobreak\ \rm{eV})$ (95% CL)
|  |  $g_{a\gamma}<10^{-13}$ GeV-1 (95% CL)
|  | for $10^{-13}$ eV $<m_{a}\lesssim 2\times 10^{-12}$ eV
Light Relic Particles |  |
Free-streaming Relativistic | $N_{\rm{eff}}$ | $\sigma(N_{\rm{eff}})=0.014$
Inflation |  |
Inflationary Magnetic Fields | $B_{\rm{SI}}$ |  $\sigma(B_{\rm{SI}})=0.036$ nG
Primordial Non-Gaussianity | $f_{\mathrm{NL}}^{\rm local}$ | $\sigma(f_{\mathrm{NL}}^{\rm local})=0.26$
Primordial Gravitational Waves | $r$ | $\sigma(r)=0.005$
Dark Energy |  |
Dark Energy Equation of State | $w$ | $\sigma({w})=0.005$
Neutrino Mass |  |
Sum of Neutrino Masses | $\Sigma m_{\nu}$ |  $\sigma({\Sigma m_{\nu}})=13$ meV
Other Beyond Standard Model |  |
Isotropic Birefringence | $\beta$ |  $\sigma({\beta})=0.035$ arcmin
Anisotropic Birefringence | $A_{\alpha}$ |  $\sigma(A_{\alpha})=1.4\times 10^{-6}$ deg2
Astrophysics |  |
Planetary Studies |  | Detect dwarf-size planets 100s of AU from Sun
|  | Detect Earth-sized planets 1000s of AU from Sun
|  | Detect exo-Oort clouds around other stars
Evolution of Gas |  | Probe gas physics of halos out to $z\sim 2$
|  | and with masses below $10^{12}$ M⊙
Transient Sky |  | Source flux $>4$ mJy at 150 GHz ($8\sigma$ daily limit)
Catalog of Galaxies |  | Source flux $>0.5$ mJy at 150 GHz ($10\sigma$ limit)

  * •

a CMB-HD has several methods to constrain axion-like particles (see Sections
3.1,3.2, and 3.3).

###### Contents

  1. 1 Executive Summary
  2. 2 Overview of CMB-HD Key Science Objectives
    1. 2.1 Fundamental Physics of the Universe
    2. 2.2 Astrophysics
  3. 3 Dark Matter and Dark Sectors
    1. 3.1 Gravitational Probe of Small-Scale Structure
    2. 3.2 Resonant Photon-ALPs Conversion
    3. 3.3 CMB Polarization Oscillation
  4. 4 Light Relic Particles
    1. 4.1 Free-streaming Relativistic Species
    2. 4.2 Fluid-like and Self-interacting Relativistic Species
  5. 5 Inflation
    1. 5.1 Inflationary Magnetic Fields
    2. 5.2 Primordial Non-Gaussianity
    3. 5.3 Primordial Gravitational Waves
  6. 6 Dark Energy and Neutrino Mass
  7. 7 Other Beyond Standard Model
    1. 7.1 Cosmic Birefringence
  8. 8 Astrophysics
    1. 8.1 Evolution of Gas
    2. 8.2 Planetary Studies
    3. 8.3 Transients
    4. 8.4 Catalog of Galaxies
  9. 9 Technical Overview
    1. 9.1 Measurement Requirements
    2. 9.2 Foreground Removal
    3. 9.3 Instrument Requirements
    4. 9.4 Instrument Design
    5. 9.5 Cost Estimates
  10. 10 Summary

##  2 Overview of CMB-HD Key Science Objectives

###  2.1 Fundamental Physics of the Universe

CMB-HD has the following science objectives in regard to fundamental physics
of the Universe:

  1. 1.

Dark Matter: Measure the small-scale matter power spectrum from weak
gravitational lensing using the CMB as a backlight; with this CMB-HD aims to
distinguish between a matter power spectrum predicted by models that can
explain observational puzzles of small-scale structure, and that predicted by
vanilla cold dark matter (CDM), with a significance of at least $5\sigma$ [4].
This measurement would be a clean measurement of the matter power spectrum on
these scales, free of the use of baryonic tracers. It would greatly limit the
allowed models of dark matter and baryonic physics, shedding light on dark-
matter particle properties and galaxy evolution [5, 6, 7]. Specifically, this
measurement would constrain fuzzy dark matter, warm dark matter, self-
interacting dark matter, and any other dark matter model that alters the
matter power spectrum on scales of $k\sim 10\leavevmode\nobreak\ $Mpc-1 [8, 5,
6, 9, 7].

Another observable emerges from the epoch of re-ionization. Compton up-
scattering of incident CMB photons by plasma along the line of sight is the
well known kinetic Sunyaev-Zeldovich (kSZ) effect. When induced by mildly non-
linear structure, this Ostriker-Vishniac (kSZ-OV) effect (which directly
probes the late-time growth of structure) leads to additional power in the CMB
damping tail. By suppressing the formation structure, alternate dark matter
models would alter the shape of kSZ-OV-induced anisotropies [10], potentially
facilitating a $2.7\times 10^{-21}\leavevmode\nobreak\ {\rm eV}$ 95% CL lower
limit to the fuzzy dark matter (FDM) mass.

  2. 2.

Axion-like Particles: Constrain or discover axion-like particles by observing
the resonant conversion of CMB photons into axions-like particles in the
magnetic fields of galaxy clusters. Nearly massless pseudoscalar bosons, often
generically called axion-like particles, appear in many extensions of the
standard model [11, 12, 13, 14, 15, 16]. A detection would have major
implications both for particle physics and for cosmology, not least because
axion-like particles are also a well-motivated dark matter candidate. CMB-HD
has the opportunity to provide a world-leading probe of the electromagnetic
interaction between axions-like particles and photons using the resonant
conversion of CMB photons into axions-like particles [17, 18, 19] in the
magnetic field of galaxy clusters [19], independently of whether axion-like
particles constitute the dark matter. CMB-HD would explore the mass range of
$10^{-13}$ eV $<m_{a}\lesssim 2\times 10^{-12}$ eV and improve the constraint
on the axion coupling constant by over two orders of magnitude over current
particle physics constraints to $g_{a\gamma}<0.1\times 10^{-12}$ GeV-1. These
ranges are unexplored to date and complementary with other cosmological
searches for the imprints of axion-like particles on the cosmic density field.

  3. 3.

Axion-like Particles: Constrain or discover axion-like dark matter by
measuring time-dependent CMB polarization rotation. Ultralight axion-like
dark-matter fields that couple to photons via $g_{a\gamma}$ cause a time-
dependent photon birefringence effect which manifests as a temporal
oscillation of the local CMB polarization angle (i.e., a local
$Q\leftrightarrow U$ oscillation in time) [20]. This rotation effect is in-
phase across the entire sky, and the oscillation period is fixed by the axion-
like particle mass (a fundamental physics parameter) to be at observable
timescales of $\sim$months to $\sim$hours for masses in the range
$10^{-21}\,\textrm{eV}\lesssim m_{a}\lesssim 10^{-18}\,\textrm{eV}$. Being a
time-dependent oscillation of the _observed_ CMB polarization pattern,
searches for this effect are not limited by cosmic variance. CMB-HD
improvements in the polarization map-depth and sky coverage promise
sensitivity improvements for this search by a couple of orders of magnitude in
the coupling $g_{a\gamma}$ as compared to existing BICEP/Keck analyses [21,
22], and exceed CMB-S4 projected reach by a factor of $\mathcal{O}(2)$.

  4. 4.

Light Relic Particles: Measure the number of light particle species that were
in thermal equilibrium with the known standard-model particles at any time in
the early Universe, i.e. $N_{\rm{eff}}$, with a
$\sigma({N_{\rm{eff}}})=0.014$. This would cross the critical threshold of
0.027, which is the amount that any new particle species changes
$N_{\rm{eff}}$ away from its Standard Model value of 3.04. Such a measurement
would rule out or find evidence for new light thermal particles with at least
$95\%$ confidence level. This is particularly important because many dark
matter models predict new light thermal particles [23], and recent short-
baseline neutrino experiments have found puzzling results possibly suggesting
new neutrino species [24, 25].

  5. 5.

Inflation: Probe the existence of inflationary magnetic fields in the early
Universe to find evidence of inflation. The extremely tight constraint on
anisotopic birefringence provided by CMB-HD will significantly tighten the
constraints on the strength of scale-invariant primordial magnetic fields,
$B_{\rm SI}$, that originate during inflation. CMB-HD will have the
sensitivity to obtain a $1\sigma$ uncertainty of $\sigma(B_{\rm
SI})=0.036\leavevmode\nobreak\ \mathrm{nG}$, which is below the
$0.1\,\mathrm{nG}$ threshold that distinguishes between purely inflationary
and dynamo origins of the $\mu\mathrm{G}$ level magnetic fields observed in
galaxies [26]. CMB-HD will therefore have the capability to detect
inflationary PMFs with about $3\sigma$ significance or higher, or rule out a
purely inflationary origin of galactic magnetic fields at over $95\%$ CL.

  6. 6.

Inflation: Measure the primordial local non-Gaussian fluctuations in the CMB,
characterized by the parameter $f_{\mathrm{NL}}^{\rm local}$, with an
uncertainty of $\sigma(f_{\mathrm{NL}}^{\rm local})=0.26$, by combining the
kSZ signal from CMB-HD with an over-lapping galaxy survey such as from the
Vera Rubin Observatory. Reaching a target of $\sigma(f_{\mathrm{NL}}^{\rm
local})<1$ would rule out a wide class of multi-field inflation models,
shedding light on how inflation happened [27, 28, 29, 30, 31, 32]. This cross-
correlation could also resolve the physical nature of several statistical
anomalies in the primary CMB [33] that may suggest new physics during
inflation (see Ref. [34] for a review), and provide constraints on the state
of the Universe before inflation [35].

  7. 7.

Inflation: Remove 90% of the CMB B-mode fluctuations from gravitational
lensing leaving only 10% remaining, i.e. achieve $A_{\rm{lens}}=0.1$, over
half the sky. This would enable other CMB experiments with small-aperture
telescopes, such as CMB-S4, or satellite missions, such as LiteBird, to
achieve or improve on their target measurement of the amplitude of primordial
gravitational waves, given by the parameter $r$. In addition, CMB-HD can
provide an independent constraint on primordial gravitational waves with an
uncertainty of $\sigma(r)=0.005$ via polarised Sunyaev-Zel’dovich tomography.

  8. 8.

Dark Energy: Measure the dark energy equation of state with an uncertainty of
$\sigma(w_{0})=0.005$ by combining galaxy cluster abundance measurements,
galaxy cluster lensing measurements, and measurements of the primary CMB power
spectra [36, 37]. This would provide a constraint on the dark energy equation
of state to sub-percent level accuracy.

  9. 9.

Neutrino Mass: Detect the sum of neutrino masses at about $5\sigma$
significance or higher. CMB-HD has multiple pathways to detect the sum of the
neutrino masses, $\sum m_{\nu}$, which include combining cluster abundance and
primary CMB power spectra measurements as well as combining CMB lensing and
primary CMB power spectra. The former will result in an uncertainty of
$\sigma(\sum m_{\nu})=13$ meV, assuming a Planck-like prior on the optical
depth to reionization of $\sigma(\tau_{\rm re})=0.007$ [36, 37]. Given the
current lower bound of $\sum m_{\nu}\geq 58$ meV, CMB-HD will be able to
detect the sum of neutrino masses at about $5\sigma$ significance or more.

  10. 10.

Other Beyond Standard Model: Provide a world-leading constraint on isotropic
birefringence of 0.035 arcmin and on a scale-invariant birefringence power
spectrum of $1.4\times 10^{-6}$ deg2 (68% CL). High precision CMB-HD
polarization data can be used to test for new physics by searching for a
rotation of linear polarization as the CMB photons propagate to us from the
surface of last scattering, usually referred to as cosmic birefringence. The
measurement of cosmic birefringence can be used to constrain very light axion-
like particles of $m_{a}\lesssim 10^{-28}$ eV [38, 39, 40, 41, 42], the axion
string network [43], axion dark matter [44], general Lorentz-violating physics
in the context of Standard Model extensions [45], and primordial magnetic
fields through the Faraday rotation [46, 47, 48]. CMB-HD will improve
statistical errors on the isotropic and scale-invariant anisotropic
birefringence measurements by several orders of magnitude over the existing
constraints [49, 50, 51, 52, 53, 26].

###  2.2 Astrophysics

CMB-HD would also address many questions in astrophysics, such as 1.) the
evolution of gas and galaxies in the Universe. Such a survey would also 2.)
monitor the transient sky by mapping the full observing region every few days,
which opens a new window on gamma-ray bursts, novae, fast radio bursts, and
variable active galactic nuclei. Moreover, CMB-HD would 3.) provide a census
of planets, dwarf planets, and asteroids in the outer Solar System, and 4.)
enable the detection of exo-Oort clouds around other solar systems, shedding
light on planet formation. Finally, 5.) CMB-HD will provide a catalog of high-
redshift dusty star forming galaxies and active galactic nuclei over half the
sky down to a flux limit of 0.5 mJy at 150 GHz. The CMB-HD survey will be made
publicly available, with usability and accessibility a priority.

##  3 Dark Matter and Dark Sectors

###  3.1 Gravitational Probe of Small-Scale Structure

Astronomical observations have provided compelling evidence for non-baryonic
dark matter [54, 55, 56, 57, 58, 59, 60]. However, we have not been able to
create or detect dark matter in terrestrial experiments to probe its
properties directly. If dark matter only interacts with the known standard-
model Universe gravitationally, then it makes sense to explore the
gravitational direction further to understand it. An observational puzzle
seems to exist regarding the distribution of matter on small-scales (scales
below 10 kpc and masses below $10^{9}M_{\odot}$ today); there seems to be less
structure than the standard cold collisionless model of dark matter (CDM)
would predict. This may provide clues to the particle nature of dark matter,
and, in fact, many well-motivated models of dark matter can explain this
deviation from CDM [61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93,
94, 95, 96, 97].

However, measurements of the small-scale matter distribution do not
conclusively indicate a deviation from the CDM prediction. This is because
such measurements often infer the matter distribution through baryonic tracers
[98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,
114], and such tracers may not reliably map the dark matter [115, 116, 117].
Gravitational lensing offers a powerful way to map the dark matter directly.
While strong gravitational lensing is a promising method to find low-mass
dark-matter halos [118, 119, 120, 121, 122, 123, 124, 125, 126, 127], it does
face the challenge of separating the complex and often unknown structure of
the background source from the sought-after substructure signal; using strong
lensing to measure the matter power spectrum, faces a similar challenge [128,
129, 130, 131, 132, 133, 134, 135]. A method that can evade this challenge is
to measure the small-scale matter power spectrum from weak gravitational
lensing using the CMB as a backlight [7]. The CMB serves as a perfect
backlight because i) it has a known redshift, ii) is behind every object, and
iii) is a known pure gradient on the small-scales of interest. Thus this
method can provide a powerful complementary probe of dark-matter physics [7].

We show in the left panel of Figure 1 how one can distinguish between CDM and
a model of dark matter that suppresses structure on small scales, by measuring
the small-scale gravitational lensing of the CMB [7]. Including foregrounds,
one can potentially distinguish between CDM and a 1 keV warm dark matter model
or a $10^{-22}$ eV fuzzy dark matter (FDM) model at the $5\sigma$ level [4].
Such observations could also probe scattering interactions between dark matter
and a new relativistic component [93] or the scattering rate of self-
interacting dark matter [9]. Newer lensing reconstruction techniques can
potentially improve these constraints further [136, 137]. Extragalactic
foregrounds are the main source of systematic effect in this measurement, and
paths to mitigate this are discussed in [4] and in Section 9.2. Baryonic
processes can also move around the dark matter and change the shape of the
small-scale matter power spectrum; however, they likely affect the shape of
the spectrum in a way that differs from alternate dark matter models [7, 138,
139, 140, 141, 142]. Comparing the matter power spectrum of multiple
hydrodynamic simulations, each with different baryonic prescriptions, suggests
there may be a finite set of ways that baryons can change the shape of the
spectrum, characterized by just a few free parameters [142]. Given that, one
can use the shape of the power spectrum to distinguish between dark matter
models and baryonic effects. In any case,this measurement would be a clean
measurement of the matter power spectrum on these scales, free of baryonic
tracers. It would greatly limit the allowed models of dark matter and baryonic
physics, shedding light on dark-matter properties as well as galaxy evolution.

Figure 1: Left: Dark Matter: CMB-HD would generate a high-resolution map out
to $k\sim 10\leavevmode\nobreak\ h$Mpc-1 of the projected dark matter
distribution over half the sky via gravitational lensing. Shown is the CMB
lensing power spectrum for an $m\sim 10^{-22}$ eV FDM model and a CDM model.
Error bars correspond to CMB-HD expectations of 0.5 $\mu$K-arcmin noise in
temperature and 15 arcsecond resolution over $50\%$ of the sky. Figure credit:
Hồ Nam Nguyễn. Right: Axion-like Particles: Forecasted constraints on axion-
like particles from the resonant conversion of CMB photons into axions-like
particles in the magnetic fields of galaxy clusters, from oscillation of the
local CMB polarization angle, and from the kinetic SZ Ostriker-Vishniac (kSZ-
OV) sensitivity to the mass of a very light ALP (using the methods of [10]),
comparable to constraints from Lyman-$\alpha$ forest (e.g. [143]). The BICEP
curve is obtained from Eq. (15) of [22], assuming
$\kappa\rho_{0}=0.3\,\mathrm{GeV\,cm^{-3}}$. Figure credit: Suvodip Mukherjee,
Michael Fedderke, Sayan Mandal, Gerrit Farren, and Daniel Grin.

###  3.2 Resonant Photon-ALPs Conversion

The existence of axion or axion-like particles (ALPs) in nature is a
prediction from theoretical physics [11, 12, 13, 14, 15] and its discovery is
going to be a paradigm shift in the framework of theoretical physics. Several
particle physics experiments such as CERN ALP Solar Telescope (CAST) [144],
LPS-II [145], MADMAX [146], ADMX [147], CASPER [148] are looking for the
signatures of ALPs over a wide range of masses. Along with the particle
physics experiments, cosmological probes such as CMB anisotropies and large-
scale structure are exploring the gravitational effect of ALPs on the matter
density, and this is a potential probe to discover ALPs if they are the dark
matter, as discussed in Section 3.1 [149, 150, 7]. Other possibilities to
probe ALPs via cosmological observables, in some cases even if ALPs are not
the dark matter, are through their coupling with photons.

One possibility to study ALPs is to use their coupling with photons in the
presence of an external magnetic field [151, 152]. The coupling between ALPs
and photons denoted by $g_{\gamma\gamma a}$ (we will use the notation
$g_{\gamma a}$ throughout) leads to oscillations between photons and ALPs and
vice versa in the presence of an external magnetic field. This effect is one
of the cleanest windows to detect ALPs irrespective of whether it is dark
matter or not. The signatures of this non-gravitational interaction of ALPs
with photons distorts the energy spectrum of photons and can be detected
robustly from a source of radiation with a well-known energy spectrum. The
radiation field of the CMB provides us with an excellent source that can be
used to detect the distortions due to ALPs [18, 153, 19]. The ALP distortion
($\alpha$-distortion) gets imprinted on the CMB while it is passing through
the external magnetic field of the intergalactic medium (IGM) [18], inter-
cluster medium (ICM) [19], voids [18] and Milky Way (MW) [18]. The conversion
from photons to ALPs can be classified into two types, namely the resonant
conversion and the non-resonant conversion.

The resonant conversion of CMB photons into ALPs takes place when the
effective photon mass in the plasma equals the mass of the ALP. The
polarization state of the CMB photon that is parallel to the external magnetic
field gets converted into ALPs depending upon the strength of the magnetic
field. As a result, it leads to a polarized spectral distortion in the CMB
blackbody with a unique spectral shape. Also due to inhomogeneities in the
magnetic field in astrophysical systems, the observed polarized distortion
varies spatially, which leads to a unique spatial structure that is different
from any other known spectral distortions and foreground contamination. Though
the resonant conversion of CMB photons can take place in different kinds of
astrophysical systems, it can be best measured in the Milky Way [18] and
galaxy clusters [19]. More details regarding the resonant photon-ALPs spectral
distortion in Milky Way and galaxy clusters can be found in these works [18,
153, 19].

In the right panel of Figure 1, we show the expected constraints on the
photon-ALP coupling strength as a function of ALP mass for CMB-HD (red solid
line). For comparison, we have plotted constraints from upcoming CMB missions
such as the Simons Observatory [154] and CMB-S4 [155]. For masses smaller than
$\sim 10^{-13}$ eV, the constraints are shown as dotted lines since they
depend on the availability of magnetic field observations in the outskirts of
galaxy clusters; it is possible to achieve this by combining with magnetic
field measurements using radio observations. We also show the current bounds
on photon-ALP coupling from the Planck temperature map [153], CAST [156], and
SN1987A [157].

###  3.3 CMB Polarization Oscillation

Another possibility to study ALPs via the ALP-photon coupling
$\mathcal{L}\supset-\frac{1}{4}g_{a\gamma}aF_{\mu\nu}\tilde{F}^{\mu\nu}$
arises when linearly polarized light traverses a region in which there is a
varying ALP background field; in this case, this coupling generates a
birefringence effect for photons that manifests as a rotation of the linear
polarization of the light [158, 38, 39]. Since the ALP-photon coupling is a
derivative interaction, the integrated angular amplitude of this rotation
effect $\Delta\Psi$ depends only on the values of the ALP field at the end-
points of the light trajectory [38, 159, 20]:
$\Delta\Psi=\frac{1}{2}g_{a\gamma}\left(a_{\mathrm{det}}-a_{\mathrm{emit}}\right)$,
where $a_{\mathrm{emit,det}}$ are, respectively, the ALP field values at the
spacetime points where the light is emitted and detected. In the case where
the value of the ALP field changes slowly on cosmologically slow timescales,
this is the origin of the well-known ALP-induced cosmic birefringence effect
[158, 38, 39].

However, assuming the ALP is all of the dark matter, and assuming it is
constrained by small-scale structure observables [160, 161, 95] to have a mass
$m_{a}\gtrsim 2\times 10^{-21}\,\textrm{eV}$ (somewhat stronger bounds have
also appeared [143]), then since the non-relativistic ALP dark matter field
oscillation period is uniquely fixed by its mass to be
$T_{a}=2\pi\hbar/m_{a}$, it oscillates on timescales no longer than $\sim$ a
month. This is extremely rapid by cosmological standards and gives rise to two
novel effects on the CMB polarization pattern which go beyond the usual cosmic
birefringence effect [20]: a partial depolarization of the CMB driven by ALP
dark matter field oscillations around the time of CMB decoupling, and a time-
dependent oscillation of the local CMB polarization angle as measured on the
sky today driven by the oscillation of the local ALP dark matter field at the
location of the detector. The partial depolarization (or ‘washout’) effect has
been examined in [20] using Planck power spectrum data and shown to constrain
$g_{a\gamma}\lesssim
10^{-12}\,\textrm{GeV}^{-1}\times(m_{a}/10^{-21}\,\textrm{eV})$; this effect
is however limited by cosmic variance and can be improved beyond these
existing limits by at most a factor of $\mathcal{O}(3)$.

On the other hand, the oscillation effect (‘AC oscillation’) holds much more
promise [20]. The effect can be phrased as a local-on-the-sky oscillation of
the _measured_ $Q,U$ patterns [20, 21, 22] or, equivalently, an oscillation of
the _measured_ CMB polarization angle. Because the rotation of the
polarization angle is caused directly by the oscillation of the local ALP dark
matter field value, its frequency is fixed uniquely by the ALP mass (a
fundamental physics parameter), and it has a very narrow Fourier space
linewidth: $\Delta f/m_{a}\sim v_{\textsc{dm}}^{2}\sim 10^{-6}$. This
narrowband property guarantees that, for ALPs with $m_{a}\lesssim
10^{-18}\,\textrm{eV}$ (i.e., periods $\gtrsim$ hours), the rotation is phase-
coherent on timescales that exceed 100 yrs, which also vastly exceeds
observational timescales; the signal sensitivity thus builds coherently with
integration time, and can be compared phase-coherently between detectors
operating at different epochs. The coherence length of the ALP dark matter
field is also much larger than the Solar System at these ALP masses, so the
rotation can be also phase-coherently compared between different detectors
operating at different locations on Earth or in orbit. Moreover, the phase of
the rotation of the CMB polarization angle does not depend on the direction of
arrival of the light at the detector: the signal is in-phase across the entire
sky. Finally, because the signal is a temporal variation of the _measured_
$Q,U$ patterns, it is not limited by cosmic variance. CMB-HD thus holds
enormous potential for extending the reach of this possible ALP dark matter
discovery channel.

Assuming that no ALP dark matter detection occurs, the sensitivity of CMB-HD
to exclude ALP dark matter parameter space via a search for narrowband
temporal fluctuation of the CMB polarization pattern with periods of $\sim$
hours to $\sim$ months can be roughly estimated from the statistical power of
the polarization maps as follows. The amplitude of the $Q,U$ oscillation due
to the rotation effect is of order [20, 21, 22] $\Delta\\{Q,U\\}\sim
g_{a\gamma}a_{0}\\{U,Q\\}$, where $a_{0}\sim\sqrt{2\rho_{\textsc{dm}}}/m_{a}$
is the ALP field amplitude assuming that the ALP constitutes all of the local
dark matter, $\rho_{\textsc{dm}}\sim 0.3\,\textrm{GeV/cm}^{3}$. The size of
this variation should be compared to the statistical error on the full-map
measurement uncertainty of $Q,U$, which is
$\delta_{Q,U}\sim\sigma_{\textrm{pol}}/\sqrt{\Omega_{\textrm{map}}}$ with
$\sigma_{\textrm{pol}}$ the polarization map depth in $\mu$K-arcmin and
$\Omega_{\textrm{map}}$ the sky area mapped in (arcmin)2; we assume that the
noise is white. Using that the rms values of the $Q,U$ fields over the
anticipated CMB-HD map area are similar ($Q_{\textrm{rms}}\sim
U_{\textrm{rms}}$) [162], and accounting for various $\mathcal{O}(1)$ factors,
this comparison leads to a projection for the statistical sensitivity to
exclude ALP dark matter parameter space at 95%-confidence (ignoring
systematics): $g_{a\gamma}\lesssim g^{95}_{a\gamma}\sim
m_{a}\times\big{(}\sqrt{2}\sigma_{\textrm{pol}}\big{)}/\big{(}Q_{\textrm{rms}}\sqrt{\Omega_{\textrm{map}}\cdot\rho_{\textsc{dm}}}\big{)}$.
This rough estimate is a factor of $\mathcal{O}(3)$ stronger than existing
detailed BICEP/Keck analyses when the comparison is made using appropriate
parameters [21, 22], and should be considered to be accurate at that level.
Numerically, the search sensitivity assuming fiducial CMB-HD parameters is

$g^{95}_{a\gamma}\sim 2.1\times
10^{-14}\,\textrm{GeV}^{-1}\times\left(\frac{m_{a}}{10^{-21}\,\textrm{eV}}\right)\times\left(\frac{\sigma_{\textrm{pol}}}{0.76\,\mu\textrm{K-arcmin}}\right)\times\left(\frac{f_{\textrm{sky}}}{0.5}\right)^{-1/2}\times\left(\frac{Q_{\textrm{rms}}}{4\,\mu\textrm{K}}\right)^{-1},$
(1)

where $f_{\textrm{sky}}$ is the fractional sky coverage. The fiducial value
for the polarization map-depth shown above is the combined 90/150 GHz
sensitivity for CMB-HD, and we have assumed the appropriate half-sky-averaged
rms value for the $Q,U$ maps [162]. This sensitivity projection is shown in
the right panel of Figure 1, and is a couple of orders of magnitude greater
than that of existing BICEP/Keck analyses searching for this effect [21, 22].
The cognate estimate for CMB-S4 combining both narrow- and wide-field
components [163] yields a search sensitivity reduced from that of CMB-HD by a
factor of $\mathcal{O}(2)$.

##  4 Light Relic Particles

###  4.1 Free-streaming Relativistic Species

The CMB can tell us about the inventory of particles that existed in the
Universe right back to the Big Bang. This is because any light particles (with
masses less than 0.1 eV) that were in thermal equilibrium with the known
standard-model particles, at any time in the early Universe, would have left
an imprint on the CMB. Even one new species of particle as described above,
would change the effective number of light particles, $N_{\rm{eff}}$, by as
much as $\sigma({N_{\rm{eff}}})=0.027$ away from the standard model value
(assuming no significant dilution by new states beyond the standard model
particle content) [164]. If these light particles interact only very weakly,
we may never see them in laboratory experiments, and astronomical measurements
may provide the only avenue for their detection. This is particularly
important because many dark matter models predict new light thermal particles
[23, 165], and some short-baseline neutrino experiments have found puzzling
results possibly suggesting new neutrino species [24, 25].

CMB-HD can achieve $\sigma({N_{\rm{eff}}})=0.014$, which would cross the
critical threshold of 0.027. This would potentially rule out or find evidence
for new light thermal particles with $95\%$ confidence level. By combining the
CMB-HD primordial CMB measurements with the CMB-HD measurement of the small-
scale matter power spectrum discussed above, we can also potentially gain a
factor of two improvement on $\sigma({N_{\rm{eff}}})$, subject to improvements
in modelling the nonlinear matter power up to $k\sim 0.4\leavevmode\nobreak\
h$Mpc-1 [166]. Removal of foregrounds is important for achieving these
constraints, and we discuss paths to do so in Section 9.2; we note here that
the high-angular resolution and multiple frequency channels of CMB-HD,
spanning 30 to 350 GHz, help make the necessary foreground cleaning possible.

###  4.2 Fluid-like and Self-interacting Relativistic Species

We might relax the assumption that light relics only interact gravitationally,
i.e. that they are no longer free-streaming. While free-streaming light relics
induce a phase shift of the acoustic peaks in primary CMB observations [167,
168], sufficiently strong interactions can counteract this effect, and
additionally cause an increase in the amplitude of the temperature and
polarization spectra, and a scale-dependent modulation of the CMB lensing
amplitude [169, 170]. The latter effect is a particularly promising target for
CMB-HD, as the signal increases towards smaller scales, which are accessible
for CMB-HD. As such, it is expected that CMB-HD can place more stringent
constraints on the effective number of relativistic species when allowing for
interactions, e.g. in the form of fluid-like, decoupling, or recoupling
phenomenologies from neutrino self-interactions, neutrino-dark sector
interactions, or dark radiation self-interactions [171, 172, 173, 174, 175,
176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187]. Some of these
models may have the potential to alleviate the Hubble tension [188].

Figure 2: Left: Light Relic Particles: CMB-HD can achieve
$\sigma({N_{\rm{eff}}})=0.014$, which would cross the critical threshold of
0.027, ruling out or finding evidence for new light thermal particles, at any
time in the early Universe, with at least $95\%$ confidence level. Original
figure by Benjamin Wallisch from [189, 190]; modified with addition of CMB-HD
forecast. Right: Inflation: We show the forecasted $95\%$ CL upper bounds on
$B_{\rm SI}$ from anisotropic birefringence measurements for CMB-HD (thick-
dashed lines) and also CMB-S4 [26]. We compare it with the current $95\%$ CL
upper bound on $B_{\rm SI}$ (dotted black line) obtained from CMB temperature
and polarization spectra by a joint Planck and SPT analysis [191]. Figure
credit: Sayan Mandal.

##  5 Inflation

###  5.1 Inflationary Magnetic Fields

The origin of the $\mathcal{O}(\mu\mathrm{G})$ magnetic fields observed in
galaxies today is among the biggest unsolved problems in astrophysics [192,
193]. These magnetic fields could have originated in either of the following
processes:

  1. 1.

during inflation or related processes such as reheating or preheating from the
amplification of quantum vacuum fluctuations [192, 194], leading to scale-
invariant magnetic fields,

  2. 2.

during phase transitions in the early Universe, like the electroweak (EW) or
quantum chromodynamics (QCD) phase transitions, where a strong first-order
phase transition is required to generate magnetic fields [195, 196], or

  3. 3.

from weak seed fields or local plasma mechanisms in galaxies which are
amplified by galactic dynamo processes [197].

Magnetic fields generated by the first two processes are called primordial
magnetic fields (PMFs) [198]; in this scenario, the
$\mathcal{O}(\mu\mathrm{G})$ magnetic fields we observe in galaxies today are
a result of adiabatic compression during structure formation of
$\mathcal{O}(\mathrm{nG})$ PMFs present on Mpc scales after recombination.
PMFs are also an attractive way to explain the presence of weak magnetic
fields, of at least $10^{-6}\,\mathrm{nG}$ on Mpc scales, in the empty voids
between galaxy clusters [199, 200, 201], since these fields are observed to be
relatively uniformly spread within the voids.

PMFs before structure formation are sustained in the ionized plasma, which
later adiabatically collapses to form galaxies. PMFs of strength above
$0.1\,\mathrm{nG}$ would lead to $\mu\mathrm{G}$ magnetic fields in galaxies
due to flux conservation [202], i.e. $\leavevmode\nobreak\
0.1\,\mathrm{nG}=1\,\mu\mathrm{G}(10\leavevmode\nobreak\ {\rm
kpc}/1\leavevmode\nobreak\ {\rm Mpc})^{2}$, assuming a conservative
characteristic radius of baryonic matter in galaxies of 10 kpc. Since phase
transitions do not generate scale-invariant PMFs, detecting scale-invariant
PMFs ($B_{\rm SI}$) above $\sim 0.1\,\mathrm{nG}$ on $\mathrm{Mpc}$ scales
post-recombination would imply that the galactic magnetic fields originate
during inflation [202, 203, 204]. Moreover, detecting such inflationary PMFs
would be a smoking-gun signature of inflation itself since such a strong
scale-invariant PMF on Mpc scales can only be generated during inflation [193,
205]. On the other hand, if we constrain $B_{\rm SI}<0.1\,\mathrm{nG}$, the
galactic fields could not have originated purely from inflation, and would
require further amplification from galactic dynamo processes.

The strength of scale-invariant PMFs on Mpc scales can be constrained through
their imprint on the CMB [206]. PMFs induce temperature and polarization
anisotropies in the CMB [207, 208, 205], affecting their respective power
spectra. PMFs present after recombination also cause anistropic birefringence
(or Faraday Rotation) of the CMB, i.e., a rotation of the plane of
polarization of CMB photons [46, 48, 209]. Currently, scale-invariant PMFs are
constrained to be below $1.2\,\mathrm{nG}$ at $95\%$ CL from a combination of
the Planck TT, EE, and TE spectra and the BB spectrum from SPT [191]. Since
anisotropic birefringence scales as the square of the magnetic field strength
[193, 205], as opposed to the fourth power for the CMB spectra, the vastly
improved anisotropic birefringence measurement from CMB-HD (see Sec. 7.1) will
lead to the tightest bound on $B_{\rm SI}$.

Using a realistic power spectrum of PMFs that accounts for MHD turbulence
prior to recombination, one can calculate the expected anisotropic
birefringence signal from scale-invariant PMFs in order to forecast
constraints on $B_{\rm SI}$ from birefringence measurements [26]. The
forecasted $95\%$ CL upper limit on $B_{\rm SI}$ from anisotropic
birefringence for CMB-HD is shown in the right panel of Fig. 2, and compared
to the forecast for CMB-S4 and the current $95\%$ CL upper bound of
$1.2\,\mathrm{nG}$ [191]. Anisotropic birefringence measurements from CMB-HD
will achieve a $1\sigma$ uncertainty of $\sigma(B_{\rm
SI})=0.036,\mathrm{nG}$, which is well below the $0.1\,\mathrm{nG}$ threshold
distinguishing between a purely inflationary origin of galactic magnetic
fields and a scenario requiring amplification by galactic dynamos. Ruling out
Mpc scale PMFs above $0.1\,\mathrm{nG}$ will rule out inflation as the sole
origin of the galactic magnetic fields observed today, and a detection of PMFs
below $0.1\,\mathrm{nG}$ would imply an origin through galactic dynamo
processes. Conversely, detecting $B_{\rm SI}$ above $0.1\,\mathrm{nG}$ will
imply inflationary PMFs are responsible for galactic magnetic fields, and will
provide compelling evidence for inflation itself. CMB-HD will have the
capability to detect inflationary PMFs at about the $3\sigma$ level or higher,
or rule out a purely inflationary origin of galactic magnetic fields at over
$95\%$ CL.

###  5.2 Primordial Non-Gaussianity

Primordial non-Gaussianity, the departure of the primordial curvature
perturbations from Gaussianity, is a key observational target to discriminate
different models of inflation (and its alternatives). Higher-order
correlations of the primordial fluctuations are directly sensitive to the
dynamics and field content of the primordial universe. While primordial non-
Gaussianity is very small for conventional single-field slow-roll inflation
models, other theoretically attractive models predict signals that could be
observable with CMB-HD. In particular, so called local non-Gaussianity,
quantified by the parameter $f_{\mathrm{NL}}^{\rm local}$, can detect whether
light degrees of freedom other than the inflaton contribute to the observed
scalar fluctuations. A theoretically well motivated observational target is to
constrain $f_{\mathrm{NL}}^{\rm local}<1$ [27]. A detection of
$f_{\mathrm{NL}}^{\rm local}\simeq 1$ or larger requires multifield dynamics,
while $f_{\mathrm{NL}}^{\rm local}\ll 1$ favours single-field inflation. The
current leading bound, from Planck, is $f_{\mathrm{NL}}^{\rm local}=-0.9\pm
5.1$ [210].

CMB-HD will contribute to measuring primordial non-Gaussianity not by
measuring primary CMB perturbations, which will have been measured to their
cosmic variance limit in both $T$ and $E$ below $\ell=2000$ by other
experiments, but rather indirectly through secondary anisotropies. CMB-HD will
improve constraints on $f_{\mathrm{NL}}^{\rm local}$ by exploiting CMB
anisotropies from lensing and from the kinetic Sunyaev-Zeldovich (kSZ) effect.
These secondary anisotropies probe non-Gaussianity in cross-correlation with a
galaxy survey through scale-dependent bias [211] of the galaxy field and
sample variance cancellation [212] with the CMB anisotropies. This technique
has been developed for CMB lensing in [213] and for kSZ anisotropies in [29],
with the kSZ providing somewhat stronger constraints. Because of its
unprecedented mapping of secondary CMB anisotropies, CMB-HD will be the
ultimate CMB experiment for this analysis. Using the kSZ forcasting pipeline
developed in [29], we find that CMB-HD together with the LSST-Y10 gold sample
[214] from the Rubin Observatory can constrain $f_{\mathrm{NL}}^{\rm local}$
to a precision of $\sigma({f_{\mathrm{NL}}^{\rm local}})=0.26$, excluding
$f_{\mathrm{NL}}^{\rm local}=1$ at $4\sigma$ significance. In contrast, CMB-S4
plus LSST can achieve $\sigma({f_{\mathrm{NL}}^{\rm local}})=0.7$ [29]. This
constraint is limited by the galaxy sample from the Rubin Observatory, rather
than by CMB-HD, and a combination with future more high-resolution galaxy
surveys would lead to even better constraints.

###  5.3 Primordial Gravitational Waves

Figure 3: Inflation: The statistical power of the pSZ tomography is shown with
forecasts for the $95\%$ exclusion limit on the tensor-to-scalar ratio $r$. We
use a galaxy survey with specifications matching the upcoming Vera Rubin
Observatory (VRO) together with CMB surveys with specifications matching CMB-
HD (solid green line) and CMB-S4 (dot-dashed red line). The dashed blue line
corresponds to the anticipated constraints from the delensed CMB B-mode
searches on large-scales with CMB-S4. For the galaxy survey, we take 32
redshift bins within the range $0.1<z<6.0$. The photo-z errors satisfy
$\sigma_{z}=0.03$ and we model the galaxy bias by $bg(z)=0.95/D(z)$ where
$D(z)$ is the matter growth function. We assume the distribution of electrons
trace dark matter and set the survey size to $f_{\rm sky}=0.5$. We assume the
remote quadrupole can be reconstructed for modes satisfying $2\leq L\leq 20$.
The x-axis shows the increase in the constraining power of pSZ tomography from
the non-Gaussian information provided by the smallest scales accessible to
CMB-HD. Figure credit: Selim C. Hotinli.

The search for primordial gravitational waves (PGWs) through measuring their
impact on CMB polarization is one of the primary science goals of current and
the upcoming CMB missions. For the current missions, the most promising route
for the detection of the PGWs is through measuring their impact on the
contribution to the B-mode fluctuations on scales $40\mathrel{\lower
2.5pt\vbox{\hbox{$<$}\hbox{$\sim$}}}L\mathrel{\lower
2.5pt\vbox{\hbox{$<$}\hbox{$\sim$}}}1000$. For these searches, confusion from
polarised Galactic dust emission and weak gravitational lensing by large-scale
structure are significant obstacles, with the former limiting the observable
sky to a small fraction of the survey area. Dedicated studies suggest that the
tensor-to-scalar ratio $r$ will be constrained below $\lesssim 0.001$ at
$95\%$ significance with the near-future CMB experiments. The ability of CMB-
HD to measure small-scales to high accuracy provides an excellent window of
opportunity to improve these errors through a higher-quality measurement of
small-scale CMB fluctuations that can be used to remove the lensing-induced
$B$-mode polarisation more efficiently. Using CMB-HD to delens maps of
upcoming satellite missions, such as LiteBird for example, is one of the
possible routes to potentially contribute to PGW searches.

In addition to inducing large-scale B-mode fluctuations, PWGs leave a distinct
imprint on the remote quadrupole field — the CMB quadrupole observed from
different locations in the Universe [215]. The remote quadrupole field can be
measured via observing the variations of the polarised Sunyaev Zeldovich (pSZ)
effect in the CMB maps [215, 216, 217, 218]. The pSZ effect is a small-scale
CMB polarization anisotropy induced by the scattering of CMB photons off
energetic free electrons in the post-reionization Universe. The cross-
correlation of the pSZ effect with galaxy surveys (a technique referred to as
pSZ tomography) can be used to reconstruct the remote quadrupole field and
hence to measure the PWGs [215, 216]. The high precision of CMB-HD puts it in
a unique position to detect this small-scale signal and constrain PWGs,
providing a valuable method alternative to large-scale B-mode searches.
Pushing PWG searches to a ‘multiple-observable’ regime, pSZ tomography with
CMB-HD can provide a unique way to cross-validate existing PWG measurements
(or constraints) from the primary CMB, and contribute to the characterisation
of PWGs beyond exclusion limits.

In Figure 3 we demonstrate the statistical power of pSZ tomography using a
galaxy survey with specifications matching the upcoming Vera Rubin Observatory
(VRO) with CMB surveys with specifications matching CMB-S4 (dot-dashed red
line) and CMB-HD (solid green line). The ability to probe smaller scales with
CMB-HD significantly improves the prospects to detect PWGs with pSZ tomography
compared to CMB-S4, suggesting constraints comparable to primary CMB B-mode
searches may be achievable in the future. The dashed blue line corresponds to
anticipated constraints from primary CMB B-mode searches with CMB-S4. In our
forecasts we followed [216] to calculate the tensor quadrupole signal and the
reconstruction noise from pSZ tomography. We assume the remote quadrupole can
be reconstructed for modes satisfying $2\leq L\leq 20$. As the dominant
contribution to the pSZ signal-to-noise comes from the largest scales, the
measurement quality of modes around $L\sim 2$ will play an important role in
capitalising from the statistical power of pSZ tomography, and the limited
survey size can lead to a more significant effect compared to $f_{\rm{sky}}$
[215]. Kinematic contributions to the CMB polarization on small scales can
potentially bias or add noise to the small-scale pSZ measurements, while
deviations of the electron distribution from matter may reduce the statistical
power available to the pSZ measurement below arcminute scales. For the
currently accepted electron models we anticipate the increase in errors from
the former could be around a factor of 2. Future measurements of electron
profiles and distribution from ongoing FRB searches as well as kSZ and tSZ
measurements, for example, can potentially improve the statistical power of
pSZ tomography. Simulation-based studies of the prospects to reconstruct the
remote quadrupole from the CMB can help further demonstrate the benefits of
CMB-HD.

##  6 Dark Energy and Neutrino Mass

CMB-HD will generate a catalog of galaxy clusters containing close to half a
million objects, increasing the sample size by several fold compared to
current surveys. These galaxy clusters will be detected via the thermal
Sunyaev-Zel’dovich (tSZ) effect, which occurs due to inverse Compton
scattering of CMB photons off the ionized gas in galaxy clusters. This cluster
catalog will be mass-limited down to $M_{500c}\sim 3-5\times 10^{13}\ {\rm
M}_{\odot}$ with a well understood selection function even at high redshifts
($z\geq 2$) [36, 37]. Since both dark energy and the free-streaming length of
neutrinos affect the small-scale matter power spectrum, measuring the number
of clusters in multiple mass and redshift bins – i.e. the cluster abundance –
is an excellent probe of both of these parameters. These cluster abundance
measurements in combination with primary CMB power spectra ($TT/EE/TE$) offer
compelling constraints on both the sum of the neutrino masses, $\sum m_{\nu}$,
and the dark energy equation of state, $w_{0}$. One of the primary challenges
for cluster abundance measurements is the unbiased mass calibration of galaxy
clusters. CMB-HD, with its exquisite measurements of the small-scale lensing
of the CMB temperature and polarization anisotropies, will also provide sub-
percent level errors on the masses of the detected galaxy clusters.

Marginalized joint constrains on the dark energy equation of state, $w_{0}$,
and the sum of the neutrino masses, $\sum m_{\nu}$, are presented in the left
panel of Figure 4. The constraints are obtained by combining primary CMB power
spectra ($TT/EE/TE$) measurements with cluster abundance measurements using an
internal CMB-lensing mass calibration. CMB-HD, shown in yellow, can obtain
errors of $\sigma(w_{0})=0.005$ and $\sigma(\sum m_{\nu})=13$ meV [36, 37].
Given the current lower bound of $\sum m_{\nu}\geq 58$ meV, this implies CMB-
HD will be able to detect the sum of neutrino masses at about $5\sigma$
significance or higher. Other cosmological parameters and the ones governing
the observable-mass scaling relation of galaxy clusters have been marginalized
over and are not shown in the figure. A Planck-like prior on the optical depth
to reionization of $\sigma(\tau_{\rm re})=0.007$ has been assumed. Assuming
$\sigma(\tau_{\rm re})=0.002$, as expected from the proposed LiteBIRD or CORE
[219, 220, 221] missions, can improve the constraints further by a factor of
1.5. For reference, expected constraints from two surveys (S4-Wide survey from
Chile in green and S4-Ultra deep survey from the South Pole in red) of the
proposed CMB-S4 experiment are also shown.

CMB lensing power spectrum measurements are also a sensitive probe of the sum
of the neutrino masses, and offer an independent pathway to $\sum m_{\nu}$
constraints. While these measurements have a degeneracy between $\sum m_{\nu}$
and other cosmological parameters that affect structure formation, like the
matter density, $\Omega_{m}$, or $w_{0}$ [222], such degeneracies can be
broken by including external datasets, such as from baryon acoustic
oscillations.

Figure 4: Left: Dark Energy and Neutrino Mass: Marginalized constraints on the
dark energy equation of state parameter, $w_{0}$, and the sum of the neutrino
masses, $\sum m_{\nu}$, for CMB-HD (yellow) and CMB-S4 surveys. For CMB-S4,
both the Chilean wide (S4-Wide in green) and the South Pole deep (S4-Ultra
deep in red) surveys are shown. The constraints are obtained by combining
primary CMB power spectra ($TT/EE/TE$) with cluster abundance measurements. A
Planck-like $\tau_{\rm re}$ prior of $\sigma(\tau_{\rm re})=0.007$ is assumed.
Figure credit: Srinivasan Raghunathan. Right: Beyond Standard Model: Expected
constraints on anisotropic cosmic birefringence. The horizontal solid colored
lines show the forecasted $68\%$ CL bounds on the scale-invariant power
spectrum, using the statistical uncertainty on the birefringence power
spectrum for each experiment shown by the dot-dashed colored lines. The black
solid line shows the current $68\%$ CL upper bound. Cosmic birefringence can
constrain very light axion-like particles, the axion string network, axion
dark matter, general Lorentz-violating physics in the context of Standard
Model extensions, and primordial magnetic fields. Figure credit: Toshiya
Namikawa.

##  7 Other Beyond Standard Model

###  7.1 Cosmic Birefringence

CMB polarization data can be used to test for new physics by searching for a
rotation of linear polarization as the CMB photons propagate to us from the
CMB last scattering, usually referred to as cosmic birefringence. The source
of the cosmic birefringence includes axion-like particles with a very small
mass $m_{a}\lesssim 10^{-28}$ eV coupled with photons through the Chern-Simons
term [39, 40, 41, 42], the axion string network [43], axion dark matter [44],
general Lorentz-violating physics in the context of Standard Model extensions
[45], and primordial magnetic fields through Faraday rotation of the CMB
polarization [46, 47, 48]. For example, parity violating couplings between
photons and axion-like pseudoscalar particles lead to polarization and
magnetization contributions to the electromagnetic field, and if the axion
field varies spatially or temporally, then the plane of polarizaton of the CMB
photons is rotated (see Sec. 9.9 of axion review [74]). It is seen that for
axions lighter than the Hubble scale at decoupling, i.e. $10^{-28}$ eV, the
contribution to cosmic birefringence is significant [74]. Measurement of
cosmic birefringence can also constrain the coupling $g_{\alpha\gamma}$ of
axion-like dark matter to photons. These constraints scale weakly with the
fraction $F=\Omega_{a}/\Omega_{c}$ of the energy density of axion-like dark
matter to the total dark matter, such that $g_{\alpha\gamma}\propto F^{-1/2}$
[223].

If the source of the cosmic birefringence is spatially varying on the sky, the
polarization rotation will be anisotropic [39, 224, 40, 225, 226, 45]. The
isotropic and anisotropic birefringence measurements are complementary probes
in order to constrain models which source cosmic birefringence. For example,
quintessence models predict both isotropic and anisotropic cosmic
birefringence [225, 42]. In addition, the cosmic birefringence induced by some
massless scalar fields is not necessarily isotropic, and a measurement of the
anisotropic birefringence is crucial to constraining such scenarios [227,
228]. Measurements of, or tight constraints on, the relevant pseudo-scalar
fields and other phenomena can hence provide valuable insights into
fundamental physics.

Both isotropic and anisotropic cosmic birefringence have been constrained by
several CMB experiments. The isotropic cosmic birefringence measurements have
utilized $B$-modes, part of which are converted from $E$-modes by the cosmic
birefringence effect [229, 230, 231, 232]. This $E$-to-$B$ leakage introduces
non-zero odd-parity $TB$ and $EB$ power spectra which are zero in the standard
cosmological model. The systematic errors of the uniform polarization angle
calibration in several existing CMB data are, however, larger than the
statistical error [233, 234, 235, 236, 49]. To circumvent the situation, we
can also use Galactic foreground contributions in the observed odd-parity
spectra to partially break degeneracies between the polarization angle error
and cosmic birefringence signals [237], and this technique was demonstrated
using Planck data [51]. An alternative way is to use a mode coupling
introduced by gravitational lensing in the presence of the isotropic cosmic
birefringence. The expected sensitivity to the isotropic birefringence using
the mode coupling is comparable to that using the conventional $TB$ and $EB$
spectra. We can use these two methods as a cross-check for the isotropic
birefringence measurement.

Anisotropic cosmic birefringence is efficiently constrained by using the fact
that the $EB$ correlation varies with direction. This mixes together $E$ and
$B$ modes of different scales, leading to non-zero expectation values in the
off-diagonal ($\ell,m\neq\ell^{\prime},-m^{\prime}$) elements of the CMB
covariance. Cross-correlating different angular scales of $E$ and $B$ modes,
we can reconstruct the anisotropies of the cosmic birefringence signals
[238].111Other pairs of CMB anisotropies such as temperature and $B$-modes are
also correlated, but such correlations generally give lower signal-to-noise
ratios for reconstructing birefringence [239]. The power spectrum of the
reconstructed cosmic birefringence anisotropies is, however, a four-point
correlation of the CMB anisotropies and several biases must be subtracted in
future high-precision experiments [240]. Since most physically well-motivated
models of anisotropic birefringence predict a scale-invariant spectrum,
multiple works have presented constraints on the amplitude of the scale-
invariant spectrum of the cosmic birefringence using reconstruction methods;
these have made use of the WMAP $TB$ correlation [227], or the polarization
data of the POLARBEAR [241], BICEP2/Keck Array [242], and Planck [243, 244]
experiments. The current best constraint comes from ACTPol [52] and SPTpol
[53]. We note that, although the reconstruction technique will be the best way
to constrain anisotropic birefringence, several other publications [245, 246,
247, 231, 232, 44, 248] also place constraints on anisotropic birefringence by
analyzing CMB polarization power spectra.

CMB-HD will improve the constraints on the scale-invariant anisotropic
birefringence by four orders of magnitude better than the current best
constraints. The right panel of Figure 4 shows the expected constraints on the
amplitude of the scale-invariant power spectrum from future CMB experiments
(see also [191, 26]).

##  8 Astrophysics

###  8.1 Evolution of Gas

A fundamental question in astrophysics is: how did galaxies form? A critical
advance in answering this question would be measuring the density, pressure,
temperature, and velocity of the gas in and around dark matter halos out to
$z\sim 2$ and with masses below $10^{12}$ M⊙. This is because the gas in these
halos reflects the impact of feedback processes and mergers, and it serves as
a reservoir enabling star formation. However, to date we have not had such
measurements over a statistically significant sample.

CMB-HD would open this new window by measuring the tSZ and kSZ effects with
high-resolution and low-noise over half the sky (for a recent SZ review see
[249]). The tSZ signal is a measure of the thermal pressure of ionized gas in
and around dark matter halos [250, 251]. The kSZ signal measures the gas
momentum density [252]. The combination of both tSZ and kSZ measurements, with
low-noise and high-resolution across CMB-HD frequencies, would allow CMB-HD to
separately measure the density, pressure, temperature, and velocity profiles
of the gas, as a function of halo mass and redshift [253, 254, 255]. This
would probe thermal, non-thermal, and non-equilibrium processes associated
with cosmic accretion, merger dynamics, and energy feedback from stars and
supermassive black holes, and their impact on the gas [256, 257, 258, 259,
260].

Measuring the tSZ effect is also an effective way to find new galaxy clusters
and groups, as has been well-demonstrated over the past decade [261, 262,
263]. Millimeter-wave SZ measurements have an advantage over X-ray
measurements in probing gas physics because the SZ signals are proportional to
the gas density (not density squared) and the brightness of the signals are
redshift independent. This makes SZ measurements a powerful probe of the gas
in the outskirts of galaxy clusters, and in low-mass and high-redshift halos.
CMB-HD will push halo-finding to lower masses and higher redshifts, allowing
direct imaging of systems where X-ray observations would require prohibitively
long integration times. By stacking the tSZ-detected halos, CMB-HD enables
probing the gas physics in and around halos out to $z\sim 2$ and with masses
below $10^{12}$ M⊙. The circumgalactic reservoirs of $10^{12}$ M⊙ (Milky-Way-
mass) halos are predicted by multiple simulations, such as EAGLE and
Illustris-TNG, to be intimately linked to the appearance of, and activity
within, the galaxy [264, 265, 266, 267]. These and other simulations find that
galactic star-formation rates, colors, and morphologies are inextricably
linked not only to the mass in the circumgalactic medium, but also to the
location of baryons ejected beyond $R_{200,c}$, which can be uniquely
constrained by CMB-HD. Thus the science gain of such measurements is a more
complete understanding of galaxy cluster astrophysics, the physics of the
intergalactic and circumgalactic medium, and galaxy evolution.

###  8.2 Planetary Studies

The complete inventory of planets, dwarf planets, and asteroids in our own
Solar System remains an open question. CMB-HD can open a new discovery space
in our outer Solar System by detecting undiscovered Solar System bodies via
their thermal flux and parallactic motion [268]. Objects close to the Sun are
normally detected via optical observations, which are sensitive to the bodies’
reflected light from the Sun. However, objects also have internal heat that is
emitted at millimeter wavelengths. Since the flux from reflected light falls
faster with distance than directly sourced emission, CMB-HD has an advantage
over optical surveys in finding objects in the far Solar System [269]. In
particular, CMB-HD could detect dwarf-size planets hundreds of AU from the
Sun, and Earth-sized planets thousands of AU from the Sun. In combination with
optical measurements, CMB-HD would allow large population studies of the sizes
and albedos of these objects [270]. In addition, whether our Solar System, and
exo-solar systems in general, possess an Oort cloud is still unknown. The low-
noise and high-resolution of CMB-HD would enable the detection of exo-Oort
clouds around other stars, opening a new window on planetary studies.

###  8.3 Transients

CMB-HD will plan to cover 50% of the sky with a daily cadence. The sensitivity
of CMB-HD will result in an $8\sigma$ daily flux limit of 4 mJy at 150 GHz. At
this flux limit, we expect an average of 0.1 false detections from random
noise fluctuations over the full survey of 7.5 years. Note that for moving or
variable sources, source confusion from other static sources is not an issue.
The increased sensitivity of CMB-HD also allows one to probe more volume to
detect the same events compared to precursor surveys by detecting the same
sources at larger cosmological distances. Being 15 times deeper in flux
compared to CMB-S4 gains 60 times more volume to probe sources of the same
intrinsic luminosity.

Thus CMB-HD will have excellent sensitivity to bright time-variable and
transient sources in the sky. For example, CMB-HD will detect of order 100 on-
axis long gamma-ray bursts (LGRBs) [271]. These LGRBs often are bright in the
millimeter weeks before they peak in the radio, and the additional frequency
coverage can help characterize their shock behavior [272]. Jet-dominated
active galactic nuclei called blazars are bright in the millimeter and vary
significantly at about 100 GHz on week timescales [273, 274, 275]. Novae,
which are repeating thermonuclear explosions of accreting white dwarfs, are
also millimeter-bright, with expected rates of about ten per year in our
Galaxy. CMB-HD will provide unique insight into the geometry of blazars and
novae by providing polarization flux and variability information for these
systems [276, 277]. In addition, some neutron star mergers may be seen and
localized first in the millimeter band [278]. The CMB-HD survey would thus
provide useful follow-up of LIGO/Virgo triggers, and could provide blind
detections of these events [279]. Further details on the types of transient
sources CMB-HD is sensitive to can be found in [280, 281, 282, 283]. The
intent of the CMB-HD project is to provide to the astronomy community weekly
maps of the CMB-HD survey footprint, filtered to keep only small scales, and
with a reference map subtracted to make variability apparent.

###  8.4 Catalog of Galaxies

CMB-HD’s contribution to the discovery of particularly rare, dusty galaxies
may also be significant given its coverage of a large fraction of the sky at
millimeter wavelengths. Dusty Star-Forming Galaxies (DSFGs: see [284, 285] for
reviews) with star formation rates in excess of 100 $M_{\odot}$ yr-1
constitute some of the most luminous and massive galaxies in the Universe. As
prodigious star-forming galaxies they produce incredibly massive reservoirs of
dust, even at early times in the Universe’s history ($z>5-6$; [286, 287,
288]), such that their quick formation poses unique challenges for
cosmological models of massive galaxy formation, as well as our understanding
of dust production mechanisms from AGB stars, supernovae, and ISM grain
growth. While DSFGs are a well-understood population of massive star-forming
galaxies that dominate cosmic star-formation at its peak $2<z<3$ [289, 290,
291], the relative abundance of rare DSFGs at earlier times is not as well
quantified [286, 292, 293]. And though several DSFGs have been identified at
such early times [294, 286, 288, 295], the detection and characterization of
such rare, extreme sources necessitates an ambitious millimeter survey
covering a substantial fraction of the sky at depths needed to pioneer their
detection.

While the majority of DSFGs have been identified at wavelengths
$\sim$250$\mu$m–1 mm, CMB-HD’s depth at longer wavelengths (2–3 mm) translates
to a more effective strategy in identifying the highest redshift DSFGs by
filtering out the foreground [296]. The primary limitation of CMB-HD will be
its angular resolution, limited to $\sim$0.25 arcmin in beamsize. The angular
resolution limits analysis of galaxies that are relatively faint, but the
unique contribution of CMB-HD is its ability to directly detect and
characterize brighter, rarer DSFGs with S${}_{2mm}>0.5$ mJy ($10\sigma$ limit)
with source density 2$\times$102 deg-2, a quarter of which will likely be at
$z>4$ [297, 293]. Constraining the source density of such rare, early galaxies
is critical to understanding their early formation; swift follow-up with
interferometric observations can then lead to greater insight regarding the
physical evolution of their interstellar media, shedding light on what makes
these systems so unique in the first instance.

##  9 Technical Overview

###  9.1 Measurement Requirements

The technical requirements are driven by the dark matter and new light species
science targets, since those targets set the most stringent requirements. All
the other science targets benefit from and prefer these same technical
requirements, since there are no science targets that pull the requirements in
opposing directions. This results in a fortunate confluence between the
science targets presented above and the technical requirements that can
achieve them.

Sky Area: Both the dark matter and new light species science targets prefer
the widest sky area achievable from the ground, given fixed observing time [1,
164]. For the dark matter science case, the inclusion of the kSZ foregrounds
is what makes wider sky areas preferable over smaller ones [1]. In addition,
the non-Gaussianity inflation science target, searches for planets and dwarf
planets, and probing the transient sky all benefit from the largest sky areas
possible. In practice, this is about 50% of the sky, achievable from the
demonstrated site of the Atacama Desert in Chile.

Resolution: The resolution is set by the dark matter science target of
measuring the matter power spectrum on comoving scales of $k\sim 10h$Mpc-1
(these scales collapsed to form masses below $10^{9}M_{\odot}$ today) (see
Section 3.1 for details). Since CMB lensing is most sensitive to structures at
$z\sim 2$ (comoving distance away of 5000 Mpc), we need to measure a maximum
angular scale of $\ell\sim kX\sim 35,000$. This gives a required resolution of
about 15 arcseconds at 150 GHz ($\ell=\pi$/radians), translating to a 30-meter
telescope. In addition, foreground cleaning will be essential, and the most
dominant foreground will be extragalactic star-forming galaxies, i.e. the
Cosmic Infrared Background (CIB). Figure 5 shows that removing sources above a
flux cut of 0.03 mJy at 150 GHz lowers the CIB power to well below the
instrument noise. A resolution of 15 arcsecond is also needed to measure the
profiles of the gas in halos and to separate extragalactic radio and star-
forming galaxies from the gas signal. To obtain a census of objects in the
outer Solar System, we note that the parallactic motion of objects 10,000 AU
away from the Sun is about 40 arcseconds in a year, also requiring this
minimum resolution to detect the motion across a few resolution elements.

Sensitivity: The sensitivity is driven by the dark matter science target. In
order to detect with $5\sigma$ significance a deviation of the matter power
spectrum from the CDM-only prediction at a level that matches claimed
observations of suppressed structure, one requires 0.5 $\mu$K-arcmin
instrument noise
in temperature (0.7 $\mu$K-arcmin in polarization) in a combined 90/150 GHz
channel. This assumes the residual foreground levels shown in Figure 5 [4].
Conveniently, this sensitivity level also allows one to cross critical
thresholds, achieving $\sigma({N_{\rm{eff}}})=0.014$,
$\sigma(f_{\mathrm{NL}}^{\rm local})=0.26$, and $\sigma(r)=0.005$.

Table 2: Summary of Measurement Requirements for CMB-HD Survey Over Half the
Sky

Frequency (GHz) | 30 | 40 | 90 | 150 | 220 | 280 | 350
---|---|---|---|---|---|---|---
Resolution (arcmin) | 1.25 | 0.94 | 0.42 | 0.25 | 0.17 | 0.13 | 0.11
White noise level ($\mu$K-arcmin)a | 6.5 | 3.4 | 0.7 | 0.8 | 2.0 | 2.7 | 100.0

  * •

a Sensitivity is for temperature maps. For polarization maps, the noise is
$\sqrt{2}$ higher.

Largest Angular Scale: By the time CMB-HD has first light, data from the
Simons Observatory (SO) [298], which will have first light in 2024, will
already exist and be public. SO will measure temperature and E-mode maps over
half the sky to the sample variance limit in the multipole range of 30 to 3000
for temperature and 30 to 2000 for E-modes. SO will also measure these scales
at six different frequencies spanning 30 to 280 GHz. Thus there is no need for
CMB-HD to reimage these modes. Therefore the largest angular scale CMB-HD
needs to measure is driven by measuring B-modes. For all the science goals
discussed above, with the exception of the measurements of cosmic
birefringence and inflationary magnetic fields, the largest scale CMB-HD needs
to image is about 10 arcminutes ($\ell\sim 1000)$. However, to achieve the
birefringence and inflationary magnetic field measurements (see Sections 5.1
and 7.1) requires CMB-HD to measure polarization anisotropies down to
$\ell\sim 100$. This requires that the minimum multipole in temperature maps
be
$\ell\sim 1000$, and the minimum multipole in polarization maps be $\ell\sim
100$.

Frequency Coverage: The frequency coverage is driven by needing most of the
sensitivity in the frequency window that is most free from extragalactic
foregrounds, namely 90 to 150 GHz. Modern detectors can observe at two
frequencies simultaneously [299, 300, 301], so we assume we can split closely
spaced frequency bands, further helping to remove frequency-dependent
foregrounds. We also require frequency coverage at 30/40 GHz to remove
emission from radio galaxies and at 220/280 GHz to remove emission from dusty
galaxies and to cover the null frequency of the tSZ signal (at 220 GHz).
Foreground optimization studies done for SO have found optimal ratios of noise
levels given their six frequency channels, which if extrapolated to CMB-HD
would require
noise levels in temperature maps of 6.5/3.4, 0.73/0.79, and 2/4.6
$\mu$K-arcmin for the 30/40, 90/150,
and 220/280 GHz channels respectively. In addition, CMB-HD requires deeper
sensitivity at 280 GHz in order to better remove one of the main foregrounds
(the CIB). To clean the CIB to the level shown in Figure 5 requires an
additional 280 GHz channel with 3.25 $\mu$K-arcmin noise, yielding a
combined noise level of 2.65 $\mu$K-arcmin at 280 GHz (see Section 9.2 for
more detail). This 280 GHz channel can be split into a 280/350 GHz channel at
minimal cost in order to gain a 350 GHz channel with a noise level of about
100 $\mu$K-arcmin noise.

###  9.2 Foreground Removal

Figure 5: Shown are the CMB temperature power spectrum (black solid) and
relevant foregrounds at 150 GHz. The foregrounds shown are the kSZ effect from
the epoch of reionization (brown), the tSZ effect (orange), the CIB (green),
and radio sources (purple) (after removing CIB and radio sources above a flux
of 0.03 mJy). The CMB-HD instrument noise at 150 GHz is 0.8 $\mu$K-arcmin
(dashed red), and combining 150 and 90 GHz channels brings the effective noise
level to 0.5 $\mu$K-arcmin.

One of the largest challenges to achieve the key science aimed for the by CMB-
HD experiment is removal of astrophysical foregrounds. Extraglactic
foregrounds consist of the thermal and kinetic Sunyaev-Zel’dovich effects (tSZ
and kSZ), the Cosmic Infrared Background (CIB), and radio galaxies (Radio).
Galactic foregrounds consist primarily of dust and synchrotron emission from
the Milky Way.

Galactic foregrounds dominate at large scales; since CMB-HD is targeting a
minimum multipole of $\ell=1000$ for temperature and E-mode polarization maps,
the Galactic foregrounds are largely cut out of the maps with the remainder
being subdominant. This is not the case for B-mode polarization maps however,
for which CMB-HD is targeting a minimum multipole of $\ell=100$; in this case,
the seven frequency channels will be used to remove the frequency-dependent
Galactic signal.

Extragalactic foregrounds primarily impact temperature maps, and in many cases
are both an important signal for extracting fundamental physics as well as a
contaminant to other signals. The CIB consists of dusty, star-forming galaxies
emitting primarily at sub-millimeter wavelengths, and radio galaxies are
largely active galactic nuclei or other sources emitting primarily at radio
wavelengths. Both of these types of sources have significant millimeter
emission, and given the resolution of CMB-HD, they have a profile that matches
the instrumental beam. Table 3 shows the expected single-frequency $5\sigma$
flux limits CMB-HD will achieve between 30 and 280 GHz, assuming white noise
levels only.

Given the flux limits in Table 3, we assume that radio sources can be detected
and removed that are above 0.04 mJy at 90 GHz, and correspondingly 0.03 mJy at
150 GHz, assuming a spectral in- dex of -0.8 and extrapolating the 90 GHz flux
to 150 GHz. This detection threshold assumes the absence of source confusion
from blended sources; for reference, we expect the number density of radio
sources to be less than 0.07 radio source per 0.42 arcminute beam (90 GHz
resolution) and 0.03 radio source per 0.25 arcmin beam (150 GHz resolution.)
For CIB sources, we exploit the fact that CMB-HD will have a 280 GHz channel
with 2.7 $\mu$K-arcmin white noise. We find that CIB sources above 0.15 mJy at
280 GHz can be detected at the $5\sigma$ level in the 280 GHz channel; this
detection level was determined by applying a matched-filter on maps that
included confusion from other CIB sources, as well as the kSZ, tSZ, and CMB.
Assuming a spectral index of 2.6 for CIB sources, this results in the
identification of sources above 0.03 mJy at 150 GHz. Once detected, we assume
these sources can be removed using the measured flux of each source as well as
the shape of the instrumental beam. We also assume the removal of all
$3\sigma$ detected tSZ clusters. The largest challenge here will be that the
cluster tSZ signal does not follow the profile of the instrument beam.
However, given that CMB-HD has a finer resolution than the extent of most
clusters, it is well positioned to characterize mean cluster profiles.
Throughout the forecasts presented above, we do not assume the kSZ signal from
reionization will be removed. There are a number of pathways being developed
to remove the late-time kSZ effect, including exploiting cross correlations
with galaxy surveys as well as machine learning techniques.

Figure 5 shows the expected residual levels of extragalactic foregrounds in
temperature maps at 150 GHz compared to the instrument noise (dashed red) and
the lensed CMB power spectrum (black). The subtraction of Galactic and
extragalactic foregrounds will of course not be exact, and fully
characterizing the residual levels of contamination, exploring novel
foreground subtraction avenues, and exploiting knowledge from precursor
surveys such as ACT, SPT, SO, SPO, and CCAT-p will all be pursued.

Table 3: CMB-HD Single-frequency $5\sigma$ Flux Limits Assuming White Noise Frequency (GHz) | 30 | 40 | 90 | 150 | 220 | 280
---|---|---|---|---|---|---
Flux limit (mJy) | 0.14 | 0.1 | 0.04 | 0.05 | 0.1 | 0.1

###  9.3 Instrument Requirements

Given the technical requirements above needed to achieve the science targets,
the following instrument specifications below are required.

Site: The required sky area and sensitivity make Cerro Toco in the Atacama
Desert the best site for
CMB-HD. An instrument at this site can observe the required 50% of the sky; in
contrast, an instrument at the South Pole can access less than half of this
sky area. The sensitivity requirement of 0.5 $\mu$K-arcmin also requires
locating CMB-HD at a high, dry site with low precipitable water vapor to
minimize the total number of detectors needed. No site within the U.S. has a
suitable atmosphere. While a higher site than Cerro Toco, such as Cerro
Chajnantor in the Atacama Desert, might reduce the detector count further,
that may not outweigh the increased cost of the higher site.

Detectors: To reach the required sensitivity levels of 6.5/3.4, 0.73/0.79, and
2/4.6 $\mu$K-arcmin for the 30/40, 90/150, and 220/280 GHz channels
respectively, requires scaling down the SO goal noise levels by a factor of 8
[298]. SO, which is at the same site as CMB-HD, requires 30,000 detectors to
achieve its sensitivity levels in 5 years of observation [298]. Since the
noise level scales as sqrt$(N_{\rm{det}})$ and sqrt($t_{\rm{obs}}$), CMB-HD
requires 1.3 million detectors and 7.5 years of observation to
reach a factor of 8 lower noise than SO across all frequencies. An extra
280/350 GHz channel with
3.25 $\mu$K-arcmin noise increases the detector count to 1.6 million. This
assumes a 20% observing efficiency, as also assumed by SO. We note, however,
that this observing efficiency is likely pessimistic. ACT and POLARBEAR,
precursor experiments in Chile, have usually reached 17-30% observing
efficiency, and several improvements have been identified that could increase
observation efficiency. For example, some solar power could reduce downtime by
about 10%. This number also assumes a detector yield of 80% as achieved
previously; however, given the higher number of wafers and more stringent
screening, it may be feasible to get a yield of 90%.

Telescope Dish Size: To achieve the required resolution of 15 arcseconds at
about 100 GHz requires a telescope dish size of about 30-meters. The
foreground cleaning discussed above also necessitates a 30-meter dish for the
frequencies above 100 GHz, out to at least 350 GHz.

###  9.4 Instrument Design

####  9.4.1 Telescope

For systematic control, the baseline design of CMB-HD is an off-axis telescope
with a primary aperature of 32 meters. We use a crossed Dragone design because
it has a larger field-of-view (fov) than Gregorian or Cassegrain telescopes.
Although the crossed Dragone design has a far larger secondary mirror (26
meters), as shown in Figure 6, with the use of correcting cold optics
extremely large fovs are possible. Simple calculations indicate that with
efficient focal plane use ($>50$%) it could be possible to fit all the
detectors in one telescope. However, given the number of receivers required,
the baseline design consists of two telescopes.

The Cross-Dragone design of CMB-HD is largely a scaled up version of the SO
large-aperture telescope (LAT) and CCAT-Prime designs, which are currently
being manufactured (see Figure 7 for SO LAT design). The major differences
will be the mount for the CMB-HD telescopes, which will need to support more
weight than the SO LAT or CCAT-Prime. Another main difference is that CMB-HD
will require a laser metrology system to correct for thermal, gravitational,
and wind effects on timescales of tens of seconds. Such a laser metrology
system is currently being tested on the GBT 100-meter telescope at millimeter
wavelengths. Table 4 lists the detailed telescope characteristics of CMB-HD.

Figure 6: A possible design for the telescope would be a crossed Dragone
design similar to that chosen for SO and CCAT-prime. Although challenging to
build, a 30-meter version of this particular design offers a diffraction
limited field of view out to $r=0.8$ degrees at 150 GHz at the secondary
focus, and, with cold reimaging optics such as those shown on the right,
diffraction limited beams can be achieved out past a radius of 2.68 degrees at
150 GHz and even further at lower frequencies. These particular designs are
limited by the largest silicon optics currently available (45 cm) and could be
grouped together in multiple cryostats in order to ensure less down time and
greater flexibility. Figure credit: Simon Dicker. Figure 7: Shown is the
design for the SO large-aperture telescope (SO LAT). The Cross-Dragone design
of CMB-HD is largely a scaled up version of the SO LAT and CCAT-Prime
telescope designs. The main differences will be the mount for each CMB-HD
telescope, since the CMB-HD mounts will need to support more weight, and the
addition of a laser metrology system required by CMB-HD. Figure reproduced
from [302]. Table 4: Telescope Characteristics Table for CMB-HD

Telescope | Value/Summary
---|---
Main and Effective Aperture Size | 32 meter actual, 28 meter illuminated
System Effective Focal Length | f/1.9 – f/2.8
Total Collecting Area | 500–610 square meters per telescope
Field of View |  $>3.2$ degree diameter at 150 GHz
| (with cold reimaging optics)
Wavelength range | 0.86 mm to 10 mm
Optical surface figure quality (RMS) | 25 $\mu$m requirement (15 $\mu$m goal) a
Surface Coating Technique | Machined aluminum
Number of Mirrors or Reflecting Surfaces | Two
Size of each Optical Element | Primary: 32m diameter
and its Clear Aperture | Secondary: 26 m diameter
Panel dimensions | Primary: 0.75 to 2.0 m
| Secondary: 0.75 to 2.0 m
Panel surface rms (each panel) |  $<10$ microns
Mass of each Segment or Element | 10 kg/m2 per mirror panel
Total Moving Mass (on elevation bearing) | 700 – 1500 tons
Total Moving Mass (on azimuth bearing) | 2000 – 7000 tons
Mass of each Optical Element | 7000 kg mirror alone,
| 14 tons with support structure b
Panel actuator Precision and Range | Course manual adjust +-25cm;
| fine (5$\mu$m precision) adjust +-1 cm c

  * •

a Commercial laser trackers can achieve better than 10 $\mu$m measurements
along a line of sight over 30 meters; a similar system is being deployed at
the GBT. We would expect such a system to correct errors in real time at a
panel level taking care of thermal, gravitational, and wind effects on
timescales of tens of seconds.

  * •

b We baseline a carbon backup structure, and can descope to the same material
as the panels if thermal and cost constraints allow; a full study to minimize
panel gaps while ensuring that they never drop to zero is needed and will
affect the material choice.

  * •

c The range needs to be enough to take into account all thermal and
gravitational distortions with an accuracy better than our measurement of the
panel location. Lighter (more flexible but cheaper) telescope structures are
possible if real-time adjustment/measurement of mirror shapes and locations
are better.

Table 4: Telescope Characteristics Table for CMB-HD (continued)

Telescope | Value/Summary
---|---
Degrees of Freedom (mirror panels) | 5 actuators (corners/center) in Z
| and manual x,y
Degrees of Freedom (mirror) | 5 (x,y,z,tiptilt,wedge) d
Type of Mount used for Pointing and Allowed Range | az-el, -40$<$az$<$400; 0$<$el$<$180
Mass and Type of Material for Support Structure | 7 tons of carbon fiber (each mirror)
| steel telescope structure e
Optic Design | Cross-Dragone
Description of Adaptive Optics | Laser metrology system

  * •

d Note that to keep the mirrors fixed with respect to each other the secondary
mirror may be moved to obtain and maintain alignment.

  * •

e With an active measurement system one does not need low CTE materials; steel
is much more cost effective.

####  9.4.2 Receiver

The CMB-HD telescope cameras will hold about 400,000 pixels. Each pixel will
have two frequency bands and two polarizations for a total of 1.6 million
detectors. We assume in the baseline design horn-fed TES detectors, however,
MKIDs may also be a viable detector technology, which could reduce the cost
significantly. MKIDs are less complex to fabricate and are naturally
multiplexed, simplifying their readout. We note that MKIDs are currently being
used by MUSTANG-2 at 90 GHz, and TolTEC will use MKIDs at 150, 220, and 270
GHz; thus they are currently being field tested at similar frequencies and
resolution as CMB-HD. Using MKIDs at lower frequencies would require further
MKID development. CMB-HD will have four frequency band pairs: 30/40, 90/150,
220/280, 280/350 GHz. The distribution of detectors per frequency for the
first three band pairs will be similar to the ratios adopted by SO, and
achieve the noise levels given above. These ratios were calculated by
calculating target map noise for each frequency from the science requirements
and then taking into account how detector noise varies with frequency.

For a baseline receiver we adopt a design similar to that for CCAT-prime and
SO (see Figure 8). Multiple sets of cold silicon lenses re-image the telescope
focal plane while adding a 1K lyot stop, baffles for control of stray light,
and cold blocking and bandpass filters. For SO and CCAT-prime these are housed
in a single cryostat. However, for a telescope the size CMB-HD it makes sense
to group them into a number of cryostats; a single cryostat many meters across
is hard to build and impractical to transport and maintain. In addition,
recent advances in low-loss silicon [303, 304] could allow a warm first lens,
and in that case the packing density of tubes could become far greater [305],
allowing for smaller cheaper cryostats.

Figure 8: CMB-HD will adopt a similar design for its baseline receiver as that
used by SO and CCAT-Prime. Shown here is the CMB-S4 receiver design, which is
an extension of the SO LATR design; the CMB-S4 receiver has a 2.6 meter
diameter and 19 optics tubes, whereas the SO LATR has 13 optics tubes. With
the aid of a warm first lens, it is possible to focus light through smaller
vacuum windows with very little gaps between tubes - currently tens of
centimeters are needed between tubes in order to maintain the strength of the
cryostat resulting in a loss of 50% of the telescope’s focal plane. CMB-HD
will aim to increase the packing density of optics tubes. Seven receivers are
assumed to fit in the CMB-HD focal plane, which has a diameter of about 7.3
meters, for each telescope. Figure reproduced from [302].

The baseline design of CMB-HD assumes seven cryostats for each telescope, each
of which has a diameter of about 2.5 meters (including flanges). The focal
plane area is about 7.3 meters in diameter, which can contain the seven
cryostats. Each cryostat holds between 13 and 26 optics tubes (depending on a
final optimization of tube size versus cost and focal plane usage). Every
optics tube has a vacuum window, thermal-infrared blocking filters, and cold
lenses that focus the light onto an array of detectors cooled to 0.1K. Each
optics tube will hold 500 to 4000 pixels (depending on frequency) that are
sensitive to two polarizations and two frequency bands per pixel (i.e. four
detectors per pixel). Assuming $2f*\lambda$ spacing of detectors and a
conservative filling factor of the focal plane of 50% (due to gaps between
detector wafers, optics tubes, and cryostats), then with the optical
throughput of our design it is possible to fit $\sim 132,000$ pixels per
telescope. We will aim for a more optimistic filling factor of 75%, yielding
about 200,000 pixels per telescope.

Other than achieving the high packing density of detectors in the receivers,
the assumed instrumentation is based on demonstrated technology. Similar
optics tubes have been used by ACT, BICEP/Keck, POLARBEAR, and SPT. ACT has
demonstrated successful use of horn-coupled dichroic, dual-polarization
pixels. ACT has also successfully cooled their detector arrays to 0.1K using a
dilution refrigerator. Pulse-tube cryocoolers cool the optics and thermal
shields to 4K. Horn-coupled TES detectors read out by time-domain multiplexing
have the highest technology readiness level and have been used in CMB
experiments like ABS, ACTPol, Advanced ACTPol (AdvACT), CLASS, and SPTpol.
CMB-HD will cover a spectral range of 30 to 350 GHz. Table 5 lists the
characteristics of the receiver instrumentation.

Table 5:  Receiver Instrumentation for CMB-HD Item | Value
---|---
Type of Instrument | Polarization-sensitive bolometer cameras;
| Seven cameras per telescope
Spectral Range | Dichroic pixels at 30/40, 90/150,
| 220/280, and 280/350 GHz
Optics Tubes | 91 to 182 per telescope,
| each tube with about 40 cm clear aperture;
| Distributed roughly in the ratio of 1:4:2:2 for
| 30/40, 90/150, 220/280, and 280/350 respectively
Number of Detectors, type, and pixel count | 1.6 million TES bolometers (400,000 pixels)
Thermal or Cryogenic Requirements | 0.1K (Pulse tubes to 4K + Dilution fridge)
Size/Dimensions (for each instrument) | 2.5m diameter, 2–3m long
Instrument average science data volume / day | 190 TB/day uncompressed
Instrument Field of View | 1 degree diameter (each)
Development Schedule | 2 years design + 2 years construction
| (construction schedule will be limited by
| detector/readout fabrication)

####  9.4.3 Site

Figure 9: Cerro Toco in the Atacama Desert. Top: Photo courtesy of Debra
Kellner. Bottom: Image from Google Earth. Telescopes pictured are the Atacama
Cosmology Telescope (ACT), POLARBEAR/Simons Array, and the Cosmology Large
Angular Scale Surveyor (CLASS). Also shown is the site of the funded Simons
Observatory (SO).

Cerro Toco in the Atacama Desert is the best site to achieve the science of
CMB-HD [e.g. 306]. It is 5200 meters above sea level and sits on public
Atacama Astronomical Park (AAP) land. An instrument at this site can survey
the required 50% of the sky. The sensitivity requirement of 0.5 $\mu$K-arcmin
also requires locating CMB-HD at a high, dry site with low precipitable water
vapor to minimize the total number of detectors needed. No site within the
U.S. has a suitable atmosphere. While a higher site than Cerro Toco, such as
Cerro Chajnantor in the Atacama Desert, might reduce the detector count
further, that likely does not outweigh the increased cost of construction and
operations at the higher site.

Figure 9 shows the existing CMB telescopes already on this plateau, namely
ACT, POLARBEAR/Simons Array, and the Cosmology Large Angular Scale Surveyor
(CLASS). Also shown is the location of the funded SO, which is expected to
have first light in 2024. In addition to the footprints of these existing and
planned telescope facilities, there is about 300,000 square feet of available
level ground at the Cerro Toco site that is appropriate for supporting
telescopes and accompanying buildings. SO will build two new buildings at this
site, one that includes a high-bay lab (11m x 8m x 8.5m high) that can support
an 8-ton crane, as well as one that includes a control room and office. These
buildings are designed to satisfy engineering code IBC-2009, with maximum
allowed winds of 90 mph. CMB-HD would build at least two new buildings,
roughly similar in scope to the SO buildings.

Regarding the atmospheric characteristics of the site, Cerro Toco is one of
the driest places on Earth, which is a necessity to achieve the science of
CMB-HD. This site has high atmospheric transmittance and low atmospheric
emission across the relevant millimeter-wave frequencies; this has been
studied extensively as discussed in [307, 308]. The Cerro Toco site has been
used for over a decade by ACT and POLARBEAR/Simons Array. As a result, how the
atmosphere impacts the noise properties of existing instruments has been well
quantified, and this information was propagated into the detector requirements
for CMB-HD discussed in Section 9.3.

Table 6:  CMB-HD WBS at Level 2 with Definitions  Work Breakdown Structure | Definitions
---|---
1.1 - Project Management | Management and systems engineering during the
| construction phase
1.2 - Telescopes | Materials, equipment, labor, and travel associated with
| the design and construction of the telescopes
1.3 - Telescope Receivers | Materials, equipment, labor, and travel associated with
| the design, fabrication, assembly, and testing of the receivers
1.4 - Detectors and Readout | Fabrication, assembly, and testing of the detectors and
| cold and warm readout electronics
1.5 - Data Acquisition | Delivery of the control systems for the observatories
| and data acquisition
1.6 - Data Management | Maintenance of site computing, networking and
| data storage; staff for data acquisition, pipeline
| development, and map making
1.7 - Site Infrastructure | Materials, equipment, labor, and travel needed to manage
| and oversee construction activities at the site
1.8 - Integration and Testing | On-site integration and commissioning of the telescopes
| and infrastructure
Table 7:  Project Cost Estimates for CMB-HD Instrumentation and Construction — US Only  Project Item (WBS 1) | Y1 | Y2 | Y3 | Y4 | Y5 | Y6 | Y7 | Y8 | Y9 | Y10 | Total ($M)
---|---|---|---|---|---|---|---|---|---|---|---
1.1 Project Management | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 100
1.2 Telescopes |  |  |  |  |  | 400 |  |  |  |  | 400
1.3 Telescope Receivers |  |  |  | 20 | 20 | 20 | 20 | 20 |  |  | 100
1.4 Detectors & Readout |  |  |  | 64 | 64 | 64 | 64 | 64 |  |  | 320
1.5 Data Acquisition |  |  | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8
1.6 Data Management | 2.4 | 2.4 | 2.4 | 2.4 | 2.4 | 2.4 | 2.4 | 2.4 | 2.4 | 2.4 | 24
1.7 Site Infrastructure |  |  |  | 10 | 10 | 6 | 6 | 6 | 6 | 6 | 50
1.8 Integration & Testing |  |  |  |  | 4 | 4 | 4 | 4 | 4 |  | 20
Total |  |  |  |  |  |  |  |  |  |  | 1022

###  9.5 Cost Estimates

Table 6 provides the CMB-HD WBS at Level 2 with definitions. The CMB-HD
instrument and site cost is shown in Table 7 with 2019 estimates. Much of the
cost is in fabricating the detectors and their readout electronics. For
detector cost comparison, CMB-HD will have a factor of 3.2 more detectors than
the proposed CMB-S4 experiment (1600k for $320 million versus 500k for $100
million). However, there are two avenues that could potentially reduce this
cost. One is that over the next several years, as upcoming experiments such as
SO require tens of thousands of detectors, the mass production of detectors
may drop the cost. The other is that MKIDs, a detector technology alternate to
TES devices, are currently being tested on-sky at millimeter wavelengths
[309]. If MKID detector technology matches in practice to its promise, then
the detector cost may drop by a factor of a few due to simplified readout and
fabrication. Thus, further development of MKID technologies and high frequency
(350 GHz) technologies in the coming years will further enable this project.

Two 30-meter-scale off-axis, crossed Dragone telescopes are costed at $400
million. The telescope receivers are estimated at $100 million (roughly a
factor of 3 higher than estimated for CMB-S4). Project management is estimated
at $10 million per year over ten years, and site infrastructure is estimated
at $50 million total. Data management and data acquisition are estimated at 12
FTEs/year and 4 FTEs/year, respectively, assuming $200,000 per FTE (including
40% for benefits and 60% for overheads).

##  10 Summary

CMB-HD is an ambitious leap beyond previous and upcoming ground-based
millimeter-wave experiments. It will allow us to cross critical measurement
thresholds and definitively answer pressing questions about dark matter and
dark sectors, light particle species, inflation, dark energy, neutrino mass,
and other beyond standard model physics. In addition, CMB-HD can open new
windows on galaxy evolution, planetary studies, and transient phenomena. The
CMB-HD project also recognizes the productivity benefit of an engaged
collaboration, and is committed to fostering a culture that enables this. The
CMB-HD survey will be made publicly available, and the project will prioritize
usability and accessibility of the data by the broader scientific community.

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