# Perspectives on fundamental cosmology from Low Earth Orbit and the Moon

Gianfranco Bertone<EMAIL_ADDRESS>Gravitation Astroparticle Physics
Amsterdam (GRAPPA),
Institute for Theoretical Physics Amsterdam and Delta Institute for
Theoretical Physics,
University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
Oliver L. Buchmueller<EMAIL_ADDRESS>Imperial College London,
Exhibition Rd, South Kensington, London SW7 2BX, United Kingdom  Philippa S.
Cole<EMAIL_ADDRESS>Gravitation Astroparticle Physics Amsterdam (GRAPPA),
Institute for Theoretical Physics Amsterdam and Delta Institute for
Theoretical Physics,
University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

###### Abstract

The next generation of space-based experiments will go hunting for answers to
cosmology’s key open questions which revolve around inflation, dark matter and
dark energy. Low earth orbit and lunar missions within the European Space
Agency’s Human and Robotic Exploration programme can push our knowledge
forward in all of these three fields. A radio interferometer on the Moon, a
cold atom interferometer in low earth orbit and a gravitational wave
interferometer on the Moon are highlighted as the most fruitful missions to
plan and execute in the mid-term.

dark matter — inflation — dark energy — space-based experiments

## Introduction

The standard cosmological model provides a simple framework to explain a
variety of observations, ranging from sub-galactic scales to the size of the
observable universe. Yet many open questions remain: the model relies on an
unknown mechanism for the production of perturbations in the early universe,
on an unknown matter component, generically referred to as dark matter, and on
an unknown mechanism that leads to an accelerated expansion of the universe,
generically referred to as dark energy.

The next generation of space-based experiments are our best chance of
unveiling these mysteries. A united front of low earth orbit and lunar
missions, as outlined in the European Space Agency’s (ESA) Human and Robotic
Exploration (HRE) European Space Agency (2021), will break unprecedented
ground on all of these fronts. Alongside the Laser Interferometer Space
Antenna Amaro-Seoane et al. (2017), a radio interferometer on the Moon, a cold
atom interferometer in low earth orbit and a gravitational wave interferometer
on the Moon would provide a full-coverage approach to unravelling the key open
questions in cosmology today.

In section Key knowledge gaps the key knowledge gaps in cosmology are
highlighted, in section Priorities for the space programme specific
suggestions for experiments that should be the priorities for ESA’s space
programme and which questions they will answer are laid out, before concluding
and discussing the future outlook in section Future outlook and summary.

## Key knowledge gaps

### Inflation

The theory of inflation is arguably the most promising model of the physics of
the early universe Guth (1981). The paradigm postulates that quantum
fluctuations went on to seed the cosmological perturbations that we see
imprinted on the Cosmic Microwave Background (CMB) and were the beginnings of
all of the structure in the universe today. And yet, much remains to be
understood about the properties of the quantum field that supposedly led to
the initial period of exponential expansion of the universe. Whilst the
paradigm is fully consistent with cosmological data et al. (2003a, b);
Collaboration (2020), we still currently lack direct smoking-gun evidence
supporting it, as well as a specific model for how one or more scalar fields
drove the expansion.

On large scales, $k\sim 10^{-3}–\,0.1\,{\rm Mpc^{-1}}$, observations of the
CMB temperature anisotropies by Planck Collaboration (2020) have confirmed to
incredible precision that density perturbations were small (fluctuations of
order $10^{-5}$) and almost scale-invariant. The simplest single-field, slow-
roll models of inflation are able to describe this spectrum of the density
perturbations. However, deviations from scale-invariance on small scales could
indicate a more complicated model that exhibits a feature in the inflationary
potential. Such models could have interesting observational signatures, such
as ultra-compact mini-haloes et al. (2016a); Bringmann  _et al._ (2012) or
primordial black holes García-Bellido and Morales (2017). Furthermore,
primordial non-Gaussianity has been constrained to be small, $f_{\rm
NL,local}=-0.9\,\pm\,5.1$, on large scales Planck Collaboration (2020). This
constraint has limited the viability of many models of inflation that
predicted larger values of primordial non-Gaussianity, for example DBI
inflation and EFT inflation Chen (2010); Renaux-Petel (2015). However,
reaching the $f_{\rm NL,local}<1$ threshold will provide strong evidence that
observations are not consistent with multi-field models of inflation Byrnes
and Choi (2010). The final piece of the puzzle can be provided by the tensor-
to-scalar ratio, which is currently constrained to be less than 0.1
Collaboration (2020), a measurement of which would indicate the energy scale
at which inflation happened.

### Dark matter

Similarly, the existence of dark matter is supported by a wide array of
independent observations, but we still know very little about the fundamental
nature of this elusive component of the universe. In the past four decades, a
strong effort went into the search for a particular class of candidates:
weakly interacting massive particles Schumann (2019). However, no experiment
has yet found evidence for these particles, and attention has turned to
different classes of dark matter candidates in regions of parameter space
where they would have evaded strong constraints from direct detection before
now, for example axion-like-particles (ALPs) Choi  _et al._ (2021); Ringwald
(2014); Irastorza and Redondo (2018) or primordial black holes (PBHs) Bertone
and Tait (2018).

Axion-like-particles are in particular a popular dark matter candidate Choi
_et al._ (2021); Ringwald (2014); Irastorza and Redondo (2018). The QCD
(quantum chromodynamics) axion was first postulated in the 70s to solve the
strong CP problem Chadha-Day  _et al._ (2021). However, ALPs more generally,
often motivated by string theories in which ultra-light particles are
ubiquitous, display the qualities required to explain all or part of the dark
matter. Whilst searches for the standard axion with a mass of order of a few
hundred keV have yielded no detections, “invisible” axions with very small
masses are still viable candidates. Search strategies vary depending on the
mass of the axion, which can’t be theoretically predicted, but the most common
approach is to probe their interactions with electromagnetic fields and
constrain the axion-photon coupling Semertzidis and Youn (2021). Astrophysical
observations are able to look for signatures of axion to photon conversion in
the presence of electromagnetic fields, for example, by looking for such
processes in the vicinity of the magnetosphere of neutron stars Witte  _et
al._ (2021); Hook and Huang (2018); Foster et al. (2022), or their production
in the solar core, triggered by X-rays scattering off electrons and protons in
the presence of the Sun’s strong magnetic fields Moriyama et al. (1998).

For masses less than 1eV, axions are a sub-set of the broader class of ultra-
light dark matter models, with masses down to (theoretically) $10^{-24}\,{\rm
eV}$, although Lyman-alpha forest constraints have ruled out axion masses less
than $2\times 10^{-20}\,\mathrm{eV}$ Rogers and Peiris (2021), see Ferreira
(2020) for a review. Ultra-light dark matter models postulate a new ultra-
light boson, which displays wave-like properties on galactic scales, but
behaves like cold dark matter on larger scales where the cold dark matter
(CDM) paradigm has strong support from observations. The behaviour on galactic
scales, due to the Bose-Einstein condensate which forms, can have interesting
signatures that could explain small-scale problems with CDM Popolo and Delliou
(2017); Bullock and Boylan-Kolchin (2017) and would have distinctive features
for distinguishing between models such as fuzzy dark matter, self-interacting
fuzzy dark matter and superfluid dark matter Du  _et al._ (2017); Khoury
(2022).

Another promising candidate that received a lot of renewed attention after the
LIGO/Virgo observations of order 10 solar mass binary black hole mergers is
primordial black holes Bird et al. (2016); Sasaki  _et al._ (2016, 2018). They
are the only proposed explanation of dark matter that requires no new physics
beyond the standard model, which makes them an attractive candidate. However,
strong constraints have now been placed across the parameter space via
microlensing, gravitational waves and CMB observations which have essentially
ruled them out as making up the entirety of the dark matter budget in all but
one window around an asteroid mass. See e.g. Green and Kavanagh (2021) for a
review of current constraints. There is also the possibility of two-component
dark matter models that include primordial black holes and another particle,
with interesting signatures of interaction between the two Adamek  _et al._
(2019); Bertone  _et al._ (2019).

### Dark energy

Dark energy is a generic term for the mechanism responsible for the observed
accelerated expansion of the universe. One of the key questions that may bring
us closer to the identification of dark energy is whether its energy density
has remained constant throughout the history of the universe, as would be the
case if it arises from the so-called vacuum energy, or whether it evolves with
time, as appropriate for an evolving quantum field. See e.g. Mortonson  _et
al._ (2014) for a review.

A diversified experimental approach involving astronomical surveys and
gravitational waves searches are arguably our best hope to make progress in
the search for smoking-gun evidence of inflation, identification of dark
matter, and understanding of dark energy. We will highlight possibilities for
future space-based experiments that can break new ground on these frontiers.

## Priorities for the space programme

Space experiments may soon provide important clues on the nature of inflation,
dark matter and dark energy. As an overview of the current context, we list in
Table 1 some experiments that might in particular enable gravitational wave
searches for signatures of dark matter and primordial gravitational waves with
space-borne interferometers as well as indirect detection of dark matter and
probing primordial fluctuations with Moon-based radio telescopes. We choose to
focus on three key probes as most relevant in the framework of ESA’s Human and
Robotic Exploration Directorate European Space Agency (2021) to address the
knowledge gaps discussed above:

  1. A)

a radio interferometer on the Moon (RIM)

  2. B)

a space gravitational wave detector using cold atoms (AEDGE)

  3. C)

a gravitational waves interferometer on the Moon (GWIM)

Open fundamental scientific question |  | Focus of ESA HRE platform :
---
LEO, Moon, Mars, BLEO
| Context of related recent and
---
future space experiments
Short, middle or long term
Origin of primordial fluctuations | Moon | LISA, AEDGE, RIM | Middle term
Nature of dark matter | LEO | LISA, AEDGE, AEDGE pathfinder, RIM, GWIM | Middle term
Phase transitions | LEO | LISA, AEDGE | Middle term
Existence of primordial black holes | Moon | LISA, AEDGE, GWIM | Middle term

Table 1: Recommendations for addressing key questions in fundamental cosmology
with the ESA HRE programme in the short, middle and long term.

### Radio interferometer on the Moon

The most relevant experiment for ESA’s Directorate of Human and Robotic
Exploration is the radio interferometer on the Moon et al. (2014); Furlanetto
et al. (2019); Burns et al. (2019); Duke  _et al._ (1985). The rationale for
this experiment is that placing a radio telescope on the far side of the Moon
would give it access to wavelengths shorter than 30 MHz. Radiation at these
frequencies is distorted or completely absorbed by the Earth’s ionosphere. An
interferometer on the Moon will bypass this limitation, as well as shield the
instruments from the background generated by terrestrial radio sources.
Furthermore, the size of the array, which determines the resolution of the
detector, is less restricted than an Earth-based detector like the Hydrogen
Epoch of Reionization Array (HERA) et al. (2017), the Low Frequency Array
(LoFAR) van Haarlem et al., M. P. (2013) or the Square Kilometre Array (SKA)
Dewdney  _et al._ (2009).

A radio telescope on the Moon would allow us to peer into the so-called dark
ages of the universe Koopmans et al. (2019), i.e. the epoch between the
emission of the CMB and the reionization of the universe, triggered by the
formation of the first stars. By studying the redshifted 21-cm line absorption
feature, we can obtain unprecedented information on the history of
reionization, and search for the signatures of dark matter annihilation or
decay by looking for specific forms of the absorption feature Valdes  _et al._
(2007); Short  _et al._ (2020).

Furthermore, a radio interferometer on the Moon could in principle have
baselines as long as 300km, which would enable unprecedented access to
information about very small scales Bernal  _et al._ (2018); Cole and Silk
(2021); Mena  _et al._ (2019). Measuring the 21cm power spectrum would provide
a tracer for the underlying dark matter power spectrum. This could unlock
information about dark matter sub-structures, the existence of primordial
black holes, and the validity of slow-roll inflationary models. Tomographic
analysis will also enable information to be gathered at a range of redshifts,
providing new insight into the evolution of our Universe between the time of
the CMB and today.

Finally, a lunar radio telescope would allow us also to efficiently probe the
so-called primordial non-gaussianity via the 21cm bispectrum Pillepich  _et
al._ (2007); Muñ oz  _et al._ (2015); Meerburg et al. (2019), which would
provide a powerful test of the theory of inflation. 21cm observations will
complement upcoming large-scale structure surveys which will help us to
understand how structures are evolving, allowing for even more information to
be extracted from the as yet un-probed region both in terms of redshift and
access to small scales. 21cm observations from the Moon therefore add to the
line of inquiry on all three fronts: inflation, dark matter and dark energy.

Arguably the largest challenge to overcome will be how to deal with extremely
large foregrounds. They are expected to be 6 or 7 orders of magnitude larger
than the signal being sought, and therefore systematics will need to be
incredibly well understood. Extremely careful subtraction of galactic
foregrounds et al. (2009, 2010) will need to be performed so that any signal
found in the data can be confidently interpreted et al. (2016b, 2021a); Liu
_et al._ (2009); et al. (2021a).

### Cold atom interferometer

The direct detection of gravitational waves (GW) with LIGO/Virgo, that led to
the Nobel prize for Physics in 2017, has opened new opportunities for
cosmology. The space interferometer LISA has been selected to be ESA’s third
large-class mission, and it is scheduled to be launched in 2034. Experience
with the electromagnetic spectrum shows the importance of measurements over a
range of frequencies, and we note that there is a gap between the frequencies
covered by LIGO/Virgo, as well as proposed detectors Einstein Telescope and
Cosmic Explorer on Earth, and LISA in space, in the deci-Hz band.

A promising candidate to explore this frequency band is the AEDGE mission
concept et al. (2020a), which is based on novel quantum technology utilising
Cold Atom (CA) techniques. Gravitational waves alter the distance between the
cold atom clouds as they pass through the interferometer.

AEDGE will be able to probe the gravitational waves due to coalescing
intermediate mass black holes with masses $100-10^{5}\,M_{\odot}$. This could
shed light on the existence of intermediate black holes, and their potential
role as seeds for the growth of supermassive black holes Latif and Ferrara
(2016). Additionally, black holes in the pair-instability mass gap will enter
the deci-Hz range. If this gap is populated then it will motivate a deeper
understanding of supernova collapse, or the need to invoke alternative
mechanisms for producing such large black holes such as hierarchical mergers
et al. (2020b, 2022); Gerosa and Fishbach (2021). Improved constraints on
order $100M_{\odot}$ primordial black holes should also be possible, which
would complement constraints from the CMB on this mass range Poulin  _et al._
(2017).

AEDGE can also probe a wide array of dark matter candidates. Scalar field dark
matter, for instance, causes quantities such as the electron mass and the fine
structure constant to oscillate with frequency and amplitude determined by the
dark matter mass and local density. This leads to variation in the atomic
transition frequencies, which imprint on the relative phase difference between
cold atom clouds that atom interferometers measure.

Proposed AEDGE sensitivities will enable the coupling between scalar dark
matter and electrons, photons or via the Higgs-portal to be probed with up to
10 orders of magnitude improvement, with respect to current constraints from
MICROSCOPE Bergé et al. (2017), on mass ranges between $10^{-18}$ and
$10^{-12}$eV. Other couplings can also be probed, for example the axion-
nucleon coupling for axion-like DM lighter than $10^{-14}$eV, or the coupling
between a dark vector boson and the difference between baryon and lepton
number Graham  _et al._ (2016); Poddar  _et al._ (2019).

Furthermore, AEDGE offers a new channel for probing strong gravity regimes,
where any deviations from general relativity are most likely to be noticeable.
For example, precise measurements of post-Newtonian parameters would offer
powerful probes of the predictions of general relativity and searches for
deviations due to, for example, a graviton mass Will (1998). Comparing
measurements in different frequency ranges will also make possible sensitive
probes of Lorentz invariance KosteleckÃœ and Mewes (2016).

An opportunity to learn about the nature of dark matter from gravitational
wave signals can also be realised by observations of coalescing black holes in
the deci-Hz band. Intermediate mass black holes ($10^{3}–10^{5}M_{\odot}$) and
primordial black holes (of any mass) may be surrounded by dense dark matter
spikes Eda  _et al._ (2013, 2015). If these black holes form binaries with a
much lighter companion, i.e. intermediate and extreme mass ratios
($q=m_{2}/m_{1}<10^{-2.5}$), then the dark matter may imprint a dephasing on
the gravitational waveform of the inspiralling binary. The amount of dephasing
could teach us something about the nature of the dark matter surrounding the
black holes, for example whether it’s cold and collisionless, or whether it’s
an ultra-light scalar field. LISA will have sensitivity to such effects for
larger mass systems Kavanagh  _et al._ (2020); Coogan  _et al._ (2022); Ng
_et al._ (2020), future ground-based gravitational wave observatories will
have sensitivity to low-mass systems, and an experiment such as AEDGE could
bridge the gap to cover the entire frequency range and promote multi-band
searches for the same signal. The gravitational wave signal could also be
accompanied by an electromagnetic counterpart that might provide information
about an environment involving dark matter if the particle is able to convert
to radiation or interact with it in some way like it does in the case of, for
example, axions.

Possible non-black hole binary cosmological targets for the deci-Hz band
include GWs from first-order phase transitions in the early Universe, e.g.,
during electroweak symmetry breaking in modifications of the Standard Model
with additional interactions, or during the breaking of higher gauge
symmetries Zhou  _et al._ (2020). The deci-Hz frequency range could also probe
different parameter ranges for such transitions, and combining measurements
with those by other experiments like LISA or LIGO/Virgo could help unravel
different contributions, e.g., from bubble collisions, sound waves and
turbulence Jinno and Takimoto (2017); Galtier and Nazarenko (2021). Another
cosmological target for the deci-Hz band is the possible GW spectrum produced
by cosmic strings Zhou and Bian (2020). In standard cosmology this spectrum
would be almost scale-invariant, but there could be modifications due to a
non-standard evolution of the early Universe. A detection or constraint on
such observables could additionally provide clues as to the nature of dark
matter, especially in the case of ultra-light dark matter particles which are
expected to be produced alongside GWs from phase transitions in the early
Universe and topological defects such as cosmic strings.

As outlined in the Cold Atom in Space Community Roadmap Alonso et al. (2022),
AEDGE, its pathfinder experiments, and other cold-atom experiments in space
would also be able to make sensitive measurements relevant to several other
aspects of fundamental physics, including the gravitational redshift, the
equivalence principle, possible long-range fifth forces et al. (2021b); Elder
_et al._ (2016), variations in fundamental constants and popular models of
dark energy et al. (2019).

With the AION experiment in the UK Badurina  _et al._ (2020), the MAGIS
experiment in the US Abe et al. (2021), the MIGA experiment in France Canuel
_et al._ (2018), the ZAIGA experiment in China Zhan et al. (2020), as well as
the proposed European ELGAR project et al. (2020c), there is already a large
programme of terrestrial cold atom experiments in place. These experiments
serve as terrestrial pathfinders for a large-scale mission like AEDGE, and it
would be important to complement those with a dedicated technology development
programme to pave the way for space-based cold atom pathfinder experiments.
First, dedicated pathfinders could be hosted at the International Space
Station, building the foundation of a medium-class mission. This could then
lead in the long-term to a large-class mission such as AEDGE to explore the
ultimate physics potential of the deci-Hz band.

### A gravitational waves interferometer on the Moon

In addition to a cold atom interferometer such as AEDGE, a lunar-based
gravitational wave (GW) interferometer is ideal for probing GW frequencies in
the range between deci-Hz to 5 Hz, which is where both Earth- and space-based
detectors have less sensitivity Lafave and Wilson (1992); Jani and Loeb
(2021). Preliminary estimates suggest that such an instrument would allow us
to trace the expansion rate of the universe up to redshift $z\sim 3$, test
General Relativity and the standard cosmological model up to redshift $z\sim
100$, and probe the existence of primordial black holes, as well as dark
matter in neutron star cores Dasgupta  _et al._ (2021, 2020).

## Future outlook and summary

We have outlined recommendations for how the future experiments in ESA’s Human
and Robotic Exploration Directorate fit into a strategy for answering the key
fundamental questions in cosmology that we have highlighted in table 1. These
experiments will operate from either low earth orbit or the Moon, and are
ambitious plans which should take place in the middle term, to give time for
pathfinders and terrestrial experiments to pave the way for the development of
the necessary technologies to make these moonshot missions possible. With many
complementarities between experiments, European Space Agency’s (ESA) Human and
Robotic Exploration programme has the potential to make dramatic and
perspective-changing discoveries in cosmology and astroparticle physics.

## Acknowledgements

The authors thank the European Space Agency for the opportunity to contribute
this review article. P.C. acknowledges funding from the Institute of Physics,
University of Amsterdam.

### Competing interests

The authors declare no competing financial or non-financial interests.

### Author contributions

Gianfranco Bertone and Oliver Buchmueller wrote the ESA science community
white paper related to this topic, which Philippa Cole adapted to form this
perspective piece.

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