contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
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# Snowmass2021 Theory Frontier White Paper: Astrophysical and Cosmological
Probes
of Dark Matter

Kimberly K. Boddy Editor Department of Physics, The University of Texas at
Austin, Austin, TX 78712, USA  Mariangela Lisanti††footnotemark:  Department
of Physics, Princeton University, Princeton, NJ 08544, USA  Center for
Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA
Samuel D. McDermott††footnotemark:  Fermi National Accelerator Laboratory,
Batavia, IL, 60510, USA  Nicholas L. Rodd††footnotemark:  Theoretical Physics
Department, CERN, 1 Esplanade des Particules, CH-1211 Geneva 23, Switzerland
Christoph Weniger††footnotemark:  GRAPPA Institute, Institute for Theoretical
Physics Amsterdam and Delta Institute for Theoretical Physics, University of
Amsterdam, 1098 XH Amsterdam, The Netherlands  Yacine Ali-Haïmoud  Center for
Cosmology and Particle Physics, Department of Physics, New York University,
New York, NY 10003, USA  Malte Buschmann  Department of Physics, Princeton
University, Princeton, NJ 08544, USA  Ilias Cholis  Department of Physics,
Oakland University, Rochester, Michigan, 48309, USA  Djuna Croon  Institute
for Particle Physics Phenomenology, Department of Physics, Durham University,
Durham DH1 3LE, U.K.  Adrienne L. Erickcek  Department of Physics and
Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599,
USA  Vera Gluscevic  Department of Physics & Astronomy, University of Southern
California, Los Angeles, CA, 90007, USA  Rebecca K. Leane  SLAC National
Accelerator Laboratory, Stanford University, Stanford, CA 94039, USA  Kavli
Institute for Particle Astrophysics and Cosmology, Stanford University,
Stanford, CA 94039, USA  Siddharth Mishra-Sharma  The NSF AI Institute for
Artificial Intelligence and Fundamental Interactions  Center for Theoretical
Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Department of Physics, Harvard University, Cambridge, MA 02138, USA  Julian B.
Muñoz  Center for Astrophysics — Harvard & Smithsonian, 60 Garden St,
Cambridge, MA, 02138, USA  Ethan O. Nadler  Carnegie Observatories, Pasadena,
CA 91101, USA  Department of Physics & Astronomy, University of Southern
California, Los Angeles, CA, 90007, USA  Priyamvada Natarajan  Department of
Astronomy, Yale University, New Haven, CT 06520, USA  Department of Physics,
Yale University, New Haven, CT 06520, USA  Adrian Price-Whelan  Center for
Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA
Simona Vegetti  Max Planck Institute for Astrophysics, 85748 Garching bei
München, Germany  Samuel J. Witte  GRAPPA Institute, Institute for Theoretical
Physics Amsterdam and Delta Institute for Theoretical Physics, University of
Amsterdam, 1098 XH Amsterdam, The Netherlands

###### Abstract

While astrophysical and cosmological probes provide a remarkably precise and
consistent picture of the quantity and general properties of dark matter, its
fundamental nature remains one of the most significant open questions in
physics. Obtaining a more comprehensive understanding of dark matter within
the next decade will require overcoming a number of theoretical challenges:
the groundwork for these strides is being laid now, yet much remains to be
done. Chief among the upcoming challenges is establishing the theoretical
foundation needed to harness the full potential of new observables in the
astrophysical and cosmological domains, spanning the early Universe to the
inner portions of galaxies and the stars therein. Identifying the nature of
dark matter will also entail repurposing and implementing a wide range of
theoretical techniques from outside the typical toolkit of astrophysics,
ranging from effective field theory to the dramatically evolving world of
machine learning and artificial-intelligence-based statistical inference.
Through this work, the theory frontier will be at the heart of dark matter
discoveries in the upcoming decade.

##  1 Introduction

Astrophysical and cosmological observations have historically played a
critical role in the study of dark matter, underpinning our confidence that
there is a missing mass component of the Universe. The evidence that
observational measurements provide for dark matter is collected across many
length scales. The earliest hints for dark matter arose from its gravitational
effects on galaxies, explaining the observed flatness of rotation curves [1,
2, 3, 4]. Gravitational lensing has also detected dark matter surrounding
galaxy clusters [5]. On yet larger scales, the cosmic web of large-scale
surveys [6], as well as the fluctuations of the cosmic microwave background
(CMB) [7], have both been integral in the development of the cold dark matter
(CDM) paradigm, where 85% of the Universe’s matter budget is dark.

A complete theory of particle dark matter111In this white paper, we focus on
the general class of _particle_ dark matter candidates and refer the reader to
other Snowmass contributions for a description of primordial black holes
(PBHs) as a dark matter candidate. will ultimately describe how it interacts
with visible matter, as well as whether it interacts with other dark states in
its own separate sector. Moreover, any such theory will be successful on both
the largest scales of the Universe as well as the smallest (i.e., sub-
galactic) scales. Over the next decade, astrophysical and cosmological probes
will provide powerful tests of fundamental questions about dark matter,
playing a unique and complementary role to the terrestrial dark matter
experimental program. This review will focus on five specific theory questions
where concrete advancements are anticipated during this time period:

  * •

_Is the Cold Dark Matter paradigm correct?_

In the CDM paradigm, dark matter is collision-less and non-relativistic during
structure formation. A natural consequence of this is the prediction of an
abundance of low-mass dark matter halos down to $\sim 10^{-6}~{}M_{\odot}$
[8]. Observations that provide information on the matter power spectrum at
small scales and various redshifts, therefore, will play a pivotal role in
confirming the CDM hypothesis. Evidence of small-scale power suppression
could, for example, suggest that dark matter is warmer (i.e., not non-
relativistic) during structure formation [e.g. 9], is not collision-less [e.g.
10], is wave-like rather than particle-like [e.g. 11], or underwent non-
trivial phase transitions in the early Universe [e.g. 12]. As we will discuss,
upcoming astrophysical surveys have the potential to start probing halo masses
to much lower values and/or higher redshifts than previously accessible,
opening the opportunity of definitively testing the CDM hypothesis.

  * •

_Is dark matter production in the early Universe thermal?_

The observed relic abundance of dark matter can be explained through a thermal
freeze-out mechanism (see [e.g. 13, 14] for recent reviews). In this picture,
dark matter is kept in thermal equilibrium with the photon bath at high
temperatures through weak annihilation processes. Once dark matter becomes
non-relativistic, dark matter is still allowed to annihilate, but the reverse
process is kinematically forbidden. The continued annihilation of dark matter
causes its comoving number density to be Boltzmann suppressed, until it
freezes out due to Hubble expansion overcoming the annihilation rate. This
process sets the present-day dark matter abundance. Importantly, the predicted
abundance is sensitive to the detailed dark matter physics, including its
particle mass as well as its specific interactions with the Standard Model.
Weakly Interacting Massive Particles (WIMPs) provide a classic example of the
freeze-out paradigm. In this case, a ${\cal O}(\text{GeV}$–$\text{TeV})$ mass
particle that is weakly interacting yields the correct relic abundance. As we
will demonstrate, upcoming astrophysical surveys will have the opportunity to
definitively test key aspects of the WIMP hypothesis by searching for the rare
dark matter annihilation and decay products that arise from the same
interactions that set its abundance in the early Universe. A combination of
improved instruments and the so-far non-observation of WIMPs has also led to
the exploration of probing dark matter candidates that are lighter or heavier
than the canonical WIMP window, and which often have a non-thermal origin in
the early Universe. This broadening of the possible dark matter candidates
that one can search for in indirect detection will continue to be driven by
the theory community.

  * •

_Is dark matter fundamentally wave-like or particle-like?_

Model-independent arguments that rely on the phase-space packing of dark
matter in galaxies have been used to set generic bounds on its minimum allowed
mass. In particular, a fermionic dark matter candidate can have a minimum mass
of $\sim\text{keV}$ [15], while a bosonic candidate can have a minimum mass of
$\sim 10^{-23}~{}\text{eV}$ [11]. Moreover, when the dark matter mass is much
less than $\sim\text{eV}$, its number density in a galaxy is so large that it
can effectively be treated as a classical field. Oftentimes referred to as
“axions” or “axion-like particles” (ALPs), these ultra-light bosonic states
can have distinctive signatures due to their wave-like nature. The QCD axion
[16, 17, 18, 19], originally introduced to address the strong CP problem, is a
particularly well-motivated dark matter candidate for which there are clear
mechanisms for how to generate the correct abundance today [20, 21, 22, 23].
In this framework, the axion mass and coupling are fundamentally related to
each other through the symmetry-breaking scale of the theory. As we show,
upcoming searches for astrophysical axions will have the sensitivity reach to
probe highly-motivated mass ranges for the QCD axion.

  * •

_Is there a dark sector containing other new particles and/or forces?_

In a generic and well-motivated theory framework, dark matter can exist in a
“dark sector” that communicates with the Standard Model through specific
portal interactions. Within the dark sector, there can be multiple new states,
as well as new forces that mediate interactions between the dark particles.
Recent theory work has demonstrated classes of dark sector models that yield
the correct dark matter abundance (see [e.g. 24] for a review), oftentimes for
lower dark matter masses than expected for WIMPs. Dark sector models can lead
to a rich phenomenology for both astrophysical and terrestrial dark matter
searches, as we will discuss. Two properties of the dark sector where upcoming
astrophysical surveys will be able to make decisive statements are the
presence of self interactions between dark matter particles [25] and new light
degrees of freedom.

  * •

_How will the development of numerical methods progress dark matter searches?_

Given the sheer volume and complexity of data expected from astrophysical
surveys in the upcoming decade, the development of effective observational and
data analysis strategies is imperative. Novel machine learning and statistical
tools will play an important role in maximizing the utility of these datasets.
In particular, scalable inference techniques and deep learning methods have
the potential to open new dark matter discovery potential across several
frontiers. Another critical numerical component to harness the anticipated
flood of astrophysical data in the next decade is the further development of
cosmological and zoom-in simulations needed to interpret the survey results.
We will comment on how such simulations are essential for understanding the
implications of particular dark matter models on small-scale structure
formation.

This list is not intended to be comprehensive, but rather to provide well-
motivated examples of areas where fundamental advancements are expected with
upcoming astrophysical and cosmological probes. We have divided this white
paper into two separate discussions reflecting what we can learn about dark
matter from its interactions with visible matter in astrophysical systems
(Sec. 2) as well as its early-Universe behavior and its role in the formation
of structure (Sec. 3). Each section briefly reviews some of the most promising
observational probes for tackling the specific theory questions delineated
above. Sec. 4 is dedicated to the exciting advancements expected in
applications of statistics and machine learning to astrophysical studies of
dark matter. We conclude in Sec. 5.

Complementarity with additional White Papers: We note that there are a number
of white papers which contain results complementary to the discussion we
provide here. A non-exhaustive list includes Dark Matter Numerical Simulations
[26], Data-Driven Cosmology [27], Dark Matter Physics from Halo Measurements
[28], Ultra-heavy Particle Dark Matter [29], and Puzzling Excesses and How to
Resolve Them [30]. We encourage interested readers to look to these related
white papers for further details of how the search for dark matter will
proceed in the coming decade.

##  2 Dark Matter Interactions with Visible Matter

Historically, a strong motivation for the existence of an interaction between
dark and visible matter arises from the simple and compelling cosmologies
described by the WIMP miracle or freeze-in production of sterile neutrinos.
These scenarios have also long motivated indirect detection searches: the same
interactions that generate dark matter could also be occurring today and allow
it to decay or annihilate into detectable signatures arising from
astrophysical sources. However, in the past decade, a substantial
portion—although certainly not all—of the well-motivated parameter space for
these models has been excluded (see [e.g. 31, 32]). Astrophysical searches for
dark matter have broadened in perspective as the theoretical community has
realized that the potential mass and interactions dark matter could have are
much, much broader. In this section, we will highlight this paradigm shift,
demonstrating that while conventional searches continue, ideas to probe
significantly heavier and lighter dark matter are appearing and will continue
to be developed in the coming years.

###  2.1 X-ray and $\gamma$-ray Dark Matter Signatures

Figure 1: The exposure of existing and upcoming X-ray and $\gamma$-ray
instruments which can search for the decay or annihilation of dark matter.
Significant progress in the coming years is expected at ${\cal
O}(\text{TeV}$–$\text{PeV})$ energies, a full exploitation of which will
require theoretical developments in the models and spectra of heavy dark
matter. Such work will also complement instruments searching for even higher
energy photons, such as PAO [33, 34]. At ${\cal O}(\text{keV}$–$\text{GeV})$
energies, the expected observational progress is far more modest at the level
of exposure. Exposure—the product of effective area, ${\cal E}$, and
observation time, $T$—partially controls how many photons an instrument will
detect on average for a given dark matter flux. We caution that this is just
one metric by which instruments can be compared: for certain dark matter
searches, the field of view or energy resolution can be critical, and then the
improvements made at lower energies will be more substantial. Regardless,
improved analysis strategies will be crucial to further enhance the dark
matter reach for this lower band. At the top of the figure, we highlight the
approximate mass range of several canonical particle dark matter (DM)
scenarios; one can roughly associate this mass range with the corresponding
energy range of probes, although this connection is only approximate.

If the dark matter of our Universe can decay or annihilate, then one of the
most promising channels for determining its particle nature is the detection
of high-energy photons. In the past decade, considerable progress has been
made in photon-based indirect detection for dark matter with masses ${\cal
O}(\text{keV}$–$\text{TeV})$, which we will predominantly focus on in this
section. This improvement has not been solely driven by the experimental
observatories: often theoretical insights have led to dramatic leaps forward
in our ability to probe dark matter. This bidirectional approach to progress
must continue in the coming years.

The fundamental ingredient for indirect searches are observational datasets. A
partial summary of the present and future landscape is provided in Fig. 1. At
the highest energies, significant progress will be achieved beyond the
existing reach of H.E.S.S. [35], HAWC [36], and similar observatories, through
a combination of CTA [37], SWGO [38], and LHAASO [39] (the last of which is
already in operation, see [e.g. 40]). The combined dark matter discovery
potential of these telescopes is significant. CTA has the possibility to
discover the higgsino [41], one of the most well-motivated WIMP candidates.
However, its ability to do so will depend on whether or not the broad program
to understand electroweak effects for TeV scale dark matter can determine its
annihilation spectrum and cross section with sufficient accuracy [42, 43, 44,
45, 46, 47, 48, 49, 50, 51]. Observations at these energies further open the
path to probing dark matter with masses above the unitarity limit,
$m_{\chi}\gtrsim 100$ TeV [52]. The space of models, cosmologies, and
production mechanisms for such ultra-heavy dark matter is being actively
developed, see [e.g. 29]. Discovering these models requires a detailed
understanding of the spectrum of particles that emerge from their annihilation
or decay, and how those states propagate to Earth. In recent years, public
codes have been developed for the propagation of high-energy states [53, 54,
55, 56, 57]. For the spectra, the most widely used approach exploits an
analogy with colliders so that Pythia [58, 59, 60] can be used for the
calculation, as in PPPC4DMID [61, 62]. This analogy breaks down at higher
energies—indeed, existing LHAASO projections simply end at $m_{\chi}=100$ TeV
due to an absence of theoretical calculations available above that scale [63].
The first steps towards reliable spectra at higher masses has recently been
taken in [64], although there remains significant work. The importance of
these developments for $\gamma$-ray searches has been considered in [65, 66].

In the ${\cal O}(\text{keV}$–$\text{GeV})$ band, observations must be made
from space as the interaction of photons with the atmosphere does not produce
a sufficiently detectable signature on the Earth’s surface. This sets a
fundamental limitation: a 1 m2 instrument operating for a decade has an
exposure of $\sim$$10^{12.5}\,\text{cm}^{2}\,\text{s}$. At keV and GeV
energies, this is roughly the sensitivity already achieved by XMM-Newton [67,
68] and Fermi [69, 70], with smaller exposures achieved for the intervening
energies with NuSTAR [71, 72], INTEGRAL [73], and COMPTEL [74]. In the longer
term, instruments such as Athena [75], AMEGO [76], and e-ASTROGAM [77] can
improve our sensitivity, but at many energies, the best anticipated datasets
are already on disk. Progress will therefore be critically reliant on new
insights for how to exploit the data. This is happening on many fronts,
including identifying new objects in which to search for dark matter signals,
such as newly discovered Milky Way dwarfs [78, 79, 80, 81, 82, 83], galaxy
catalogs [84, 85], or dark substructure [86, 87, 88, 89, 90, 91, 92, 93, 94,
95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105], as well as the development
of techniques such as cross correlation with different datasets [106, 107,
108, 109, 110, 111, 112, 113], improvements in our modeling of diffuse
backgrounds [114, 115, 116, 117], the extension to axion searches as we
describe in Sec. 2.4, and the exploitation of the dark matter brightness of
the ambient Milky Way [118, 119, 120, 32]. To expand on a single example, in
[120] it was demonstrated that the roughly twenty years of X-ray images
collected by XMM-Newton, when combined with the insight that all of these
observations occur through a column density of the Milky Way, allowed for a
search for dark matter decay that was more than an order of magnitude stronger
than previous analyses. The results were strong enough to considerably
disfavor the longstanding 3.5 keV line dark matter anomaly [121, 122]
(although see also [123, 124]). More generally, there remains several
unexplained dark matter anomalies in this energy window whose resolution will
depend on further insights from the theory community; for an extended
discussion, we refer to [30].

An additional strategy that has been developed recently considers dark matter
that scatters and becomes captured within celestial bodies. The dark matter
can then annihilate, generating a signal that depends on the mediator between
the dark and visible sectors. If the mediator is short-lived (or
insufficiently boosted), the annihilation products will remain within the
celestial object, raising its temperature. Instead, a long-lived (or
sufficiently boosted) mediator leads to annihilation products outside the
body, which can then be searched for by telescopes. The strongest constraints
on long-lived or boosted mediator models are due to $\gamma$-ray searches, as
the $\gamma$-ray backgrounds for celestial objects are very low. An excellent
candidate is the Sun, and solar $\gamma$-ray searches have been performed
using both Fermi [125, 126, 127, 128] and HAWC [129], yielding strong
constraints on GeV$-$TeV dark matter [130, 131, 132]. Optimizing for both
proximity and size, the next best celestial body is Jupiter, and Fermi
observations have been used to constrain sub-GeV dark matter [133]. More
broadly, analogous emission from the full population of brown dwarfs and
neutron stars can constrain sub-GeV to TeV dark matter [134] (see also [135]).
These searches are inherently multimessenger: solar dark matter searches for
neutrinos have been performed with Super-Kamiokande [136], IceCube [137], and
ANTARES [138]. Above ${\cal O}(100)~{}$GeV, the neutrinos will be attenuated
as they exit the Sun, and a long-lived mediator again improves detectability
[139, 130]. The scenario involving short-lived mediators can be studied with
optical and infrared telescopes, including Hubble, JWST, and Roman
observations of neutron stars [140, 141, 142, 143, 144], white dwarfs [141,
145], population III stars [146, 147, 148, 149], and brown dwarfs and
exoplanets [150].

###  2.2 Indirect Searches with Astrophysical Neutrinos

While searches for dark matter in the electromagnetic spectrum may be more
extensively developed, there is no fundamental reason that the first discovery
could not happen through a different channel. If that channel is neutrinos,
then the coming decade will be particularly exciting.

Already the possibility of dark matter decaying or annihilating to neutrinos
can be probed from MeV to PeV masses through a combination of instruments
ranging from Borexino to IceCube. For a recent review, see [151]. The
detection of ${\cal O}(\text{TeV}-\text{PeV})$ neutrinos at IceCube is
particularly tantalizing. While the experimental collaboration has produced
limits under the assumption that the observed flux does not originate from
dark matter [152, 153], a complete understanding of where these neutrinos
originate is lacking. (Although in 2017, a $\sim 300$ TeV neutrino event was
shown to be coincident with a flaring $\gamma$-ray blazar [154], which would
make this the third extraterrestrial source ever detected in neutrinos after
the Sun and Supernova 1987A.) There has been considerable work by theorists to
determine whether the IceCube flux could have a component with a dark matter
origin, see [e.g. 155, 156, 157, 158, 54, 159, 160, 161, 162, 163], and the
question remains open.

A fundamental aspect of high-energy neutrino searches, and of high-energy
indirect detection more generally, is its multimessenger nature: generically,
a signal of heavy dark matter annihilation or decay will appear in multiple
channels. If PeV scale dark matter decays to neutrinos, there will be a
significant probability for the hard neutrinos to emit a $W$ or $Z$ boson and
thereby produce additional Standard Model final states, including photons. As
a consequence, $\gamma$-ray datasets provide important context for dark matter
interpretations of the IceCube dataset (see [e.g. 53, 164, 118]).

This multimessenger strategy will continue to future instruments that will
probe neutrinos at ever higher energies. Already, there are tools available
that make a partial accounting of the underlying physics of the unbroken
Standard Model [165, 64], which build on the observation that electroweak
effects are generically relevant for heavy dark matter [61, 62]. As discussed
for the corresponding photon signals, work remains to fully understand these
processes. The importance of such exploration is emphasized by the wide array
of upcoming observatories such as ARIANNA, RNA-G, POEMMA, Grand, IceCube-Gen2,
and KM3NET, which have the potential to probe dark matter with masses up to
the GUT scale of $10^{15}$ GeV [166, 65, 167, 168, 169].

###  2.3 Dark Matter Signals from Charged Cosmic-rays

High-energy cosmic-rays have long been a probe of new physical phenomena in
the Milky Way. This is particularly true for antimatter cosmic-rays, a field
which PAMELA and AMS-02 have brought into a precision era, providing a
challenge to our understanding of the antimatter sources and generating claims
of a possible dark matter contribution.

In antiprotons, there are claims of an excess in the AMS-02 data peaking near
10 GeV [170, 171]. The excess appears robust to systematic uncertainties on
the production cross sections, cosmic-ray injection rates, and the effects of
propagation through the interstellar medium and heliosphere [172, 173]. The
anomaly has a local significance of 3–5$\,\sigma$ and is consistent with the
possibility that it is generated by the same dark matter models which could be
generating the Galactic center $\gamma$-ray excess [170, 174, 172, 173] (a
compelling possibility given the astrophysical uncertainties for the two
signals would be uncorrelated, although see [175]). The results at present do
not account for the full correlation matrix of the dataset, although attempts
to estimate the covariance suggest that it can significantly reduce the
significance of the excess [176, 177, 178]. At present, the AMS-02
collaboration has not released their correlation matrix, which will be
critical in establishing or repudiating the antiproton excess. Looking
forward, the GAPS experiment will provide an alternative measurement of low-
energy antiprotons [179] that will improve the modeling of the propagation of
antinuclei in the interstellar medium and heliosphere [180]. More broadly, the
combination of high-precision measurements of multiple cosmic-ray species and
the observation of cosmic-ray protons and electrons from different time
periods will further reduce the astrophysical uncertainties.

For sufficiently massive dark matter, any flux of antiprotons is expected to
be accompanied by heavier anti-nuclei cosmic-rays [181, 182, 183]. While dark
matter can only provide at most a small excess over the astrophysical
backgrounds in antiprotons, the backgrounds are highly suppressed for more
massive anti-nuclei [184, 185, 186, 187, 188, 189], making them a potential
smoking gun signal of new physics. Tantalizingly, the AMS-02 collaboration has
presented results of the detection of several antihelium events [190], where
essentially no background events were expected. While tentative, if confirmed,
this result could revolutionize cosmic-ray and high-energy physics. Heavier
anti-nuclei are, however, plagued by a number of uncertainties, particularly
as related to their productions (see [e.g. 191, 192]). At present, these
uncertainties imply their predicted fluxes can vary by orders of magnitude
[181, 183]. Future low-energy collider measurements will be instrumental in
reducing those uncertainties [191], and the first such measurements have
recently been provided [193, 194].

Cosmic-ray positrons are another potential dark matter probe. Given that
positrons quickly lose their energy as they propagate in the interstellar
medium, the sources must be increasingly localized to produce higher energy
cosmic-rays. The rising positron fraction measured by PAMELA [195], Fermi
[196], and AMS-02 [197] has been widely discussed as a putative signal of dark
matter annihilation or, alternatively, of nearby pulsars or supernova remnants
(see [e.g. 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209]). Dark
matter explanations are particularly challenged by Planck measurements of the
CMB temperature and polarization power spectra [210, 211, 212] and have become
increasingly fine-tuned although not entirely ruled out (see [e.g. 213, 214]).
Regardless, AMS-02 measurements remain a highly sensitive probe of dark matter
annihilation [215]; for instance, one can search for spectral features
associated with the dark matter mass [216, 217], although these must be
interpreted carefully as astrophysical sources can also generate such features
[218, 219]. Existing and upcoming cosmic-ray and electromagnetic observations
will be used to develop a deeper understanding of the properties of positron
sources [220, 221, 222, 223, 224], which will further advance the program of
probing dark matter with cosmic-rays.

###  2.4 Axion Indirect Detection

Recent years have seen significant development in indirect probes of axion
dark matter. A common strategy is to exploit a putative axion-photon coupling.
This coupling could be detected through the decay of axions to photons (which
can be stimulated [225, 226, 227, 228, 229, 230, 231, 232] or resonantly
enhanced [233, 234, 235, 236, 237, 238, 239, 240, 241]), axion-photon mixing
in an external magnetic field [242] (which can notably also imprint an
asymmetry on the polarization spectrum, see [e.g. 243]), birefringence [244,
245, 246, 247, 248, 249, 250, 251], or the production of axions from non-
orthogonal electric and magnetic fields [252]. Axions could also couple to
matter and thereby be produced abundantly in stars via bremsstrahlung emission
[253]. This process would produce anomalous cooling in these objects, which
can then be used to constrain axion-nucleon and axion-electron interactions
[254, 255, 256, 257, 258, 259]; alternatively, these axions may convert back
into photons in the magnetic fields outside of the star, generating anomalous
high-energy emission [260]. An example of recent progress is shown in Fig. 2.

Figure 2: Recent constraints derived on the axion-photon coupling using radio
observations of the Galactic Center obtained with the Green Bank Telescope
[261] (solid red, labeled “GBT”); shown for comparison is the 10$\sigma$
discovery limit for SKA in the same frequency band (transparent red). These
results are compared with the expected QCD axion parameter space (yellow), two
benchmark QCD axion models (brown, dot-dashed), existing constraints from
haloscopes (blue) [262, 263, 264, 265, 266] and CAST [267] (grey), and
indirect searches using magnetic white dwarfs (MWDs) [260, 243].

Radio searches: The mixing of axions and photons is greatly enhanced in the
magnetospheres of neutron stars, owing to the large ambient magnetic fields
and the resonant amplification possible due to the ambient plasma [268, 269,
270, 271, 272, 227, 273, 274, 261]. The characteristic plasma mass near
typical pulsars spans $\sim$ $0.1-100$ $\mu$eV [275], which roughly
corresponds to the range of masses for which axions can simultaneously solve
the strong CP problem and constitute dark matter [276], and further to the
frequency band of modern radio telescopes. The radio signal is expected to
appear as a forest of spectral lines centered about the axion mass, with each
line arising from a single neutron star in the Galactic population [271, 261].
If dark matter is predominantly in miniclusters rather than smoothly
distributed, the events will instead appear as transients spanning hours to
weeks [277]. Initial estimates indicate that near-future radio interferometers
like the Square Kilometer Array may be capable of discovering the QCD axion
[270, 277]. Searches using existing infrastructure (including the Effelsberg
100-m telescope, the Green Bank Telescope, and the Very Large Array) are
already underway and have leading limits on the axion-photon coupling in the
mass range $1\,\lesssim m_{a}\lesssim 20\,{\rm GHz}$ [278, 279, 261] (see Fig.
2 for the most recent analysis).

Recently, there has been significant theoretical progress in our understanding
of the radio signal, including a careful treatment of photon refraction,
resonant cyclotron absorption, plasma-induced line broadening, anisotropic
response of the medium in the photon production process, and general
relativistic effects [273, 274, 280, 261]. Yet many open questions remain,
including how axions and photons mix in a highly magnetized inhomogeneous
plasma, how do charge distributions in active pulsars and magnetars impact the
radio flux, what are the properties and distributions of neutron stars in
dense dark matter environments, do we expect strong deviations from dipolar
magnetic fields (and if so how does this impact the radio signal), how are
axions distributed on astrophysical scales (i.e., do they reside in tidally
disrupted axion miniclusters, and if so what are the properties of these
objects in the Galactic Center), and how can we exploit the spatio-temporal
properties of the radio signal to improve analyses. These are questions to be
answered in the next decade, and the answers have the potential to establish
radio searches as a powerful and robust probe of axion dark matter.

X-ray and $\gamma$-ray searches: High-energy photons emitted from
astrophysical sources (including galaxies, blazars, supernovae, and quasars)
may convert to axions in galactic- and cluster-scale magnetic fields (axions
could also be produced in stellar cores [281]). The conversion probability
depends on the magnetic field strength and configuration along the photon
trajectory, as well as the plasma frequency. At sufficiently large photon
energies, the photon-to-axion conversion probability becomes ${\cal O}(1)$ and
is thus capable of generating large absorption features in the electromagnetic
spectrum. The efficiency of this conversion process decreases at lower
energies (at a fixed axion mass), generating small oscillatory features in the
observed spectrum. Using this idea, constraints on the axion-photon coupling
have been set using X-ray [282, 283, 284, 285, 286] and $\gamma$-ray [287,
288, 289, 290, 291, 292] telescopes for masses $m\lesssim 0.1$ $\mu$eV
(excluding couplings $g_{a\gamma\gamma}\gtrsim 10^{-12}\,{\rm GeV}^{-1}$ for
$m_{a}\lesssim 10^{-11}$ eV), and they apply regardless of whether or not
axions contribute to dark matter. Future progress will be aided by improved
high-energy observations and by further understanding of galactic and cluster-
scale magnetic fields.

###  2.5 Emission of Dark Sector States from Compact Objects

Standard Model particles in high-density environments, such as stars and
supernovae, can emit new weakly-coupled states that might exist beyond the
Standard Model. The particles emitted could either be dark matter themselves
or, alternatively, part of a broader weakly-coupled “dark sector,” which is
potentially necessary to endow sub-GeV dark matter with the correct relic
abundance. The emission process can result in either observable deviations
from the Standard Model predictions on short timescales or long-term global
changes to the evolution of the compact object, both of which can be
constrained. The theory frontier has long played a crucial role in bridging
the gap between astrophysical probes, complex multi-body Standard Model
calculations, and inference on new particle properties.

The paradigmatic example of “short-term” constraints comes from the successful
explosion of Supernova 1987A and the detection of neutrinos for the predicted
$\sim 10$-second-long cooling phase [293, 294]. The qualitative agreement of
this observation with Standard Model-only numerical simulations [295, 296] has
been used to constrain the properties of the QCD axion with ever-increasing
fidelity and sophistication [297, 298, 299, 300, 301, 302, 253, 303]. The
theory frontier is still grappling with these calculations. Upcoming
challenges will be centered on application of effective field theory
techniques, which promise important changes in expected rates for Standard-
Model-only processes (such as nuclear and neutrino matrix elements and
scattering rates), as well as for beyond-the-Standard-Model rates.

A successful explosion of Supernova 1987A could also have been inhibited by a
large dark sector [304, 305, 306, 303]. Broadly, Supernova 1987A provides the
strongest bounds for any number of new particles in the ${\cal
O}(1$–$100~{}\text{MeV})$ mass range, being cut off at high masses by
Boltzmann suppression from thermal production in the core, which attains
temperatures between 30–100 MeV [295, 307]. The power of these bounds at
larger couplings is generally limited by the existence of a “trapping” limit.
At couplings above the trapping limit, the new particles are more tightly
coupled than the Standard Model neutrinos and thus are unable to drain the
energy the neutrinos were observed to have taken away. Nevertheless, with the
increasing fidelity of numerical simulations [308], the region beyond the
trapping limit is a clear avenue for future theoretical and numerical
investigations.

A second type of stellar constraint pertains most relevantly to particles that
are substantially lighter and more weakly coupled than the MeV range in which
supernova limits excel. In this mass range, dark matter must generally be non-
thermal in order to avoid constraints on the number of new radiation degrees
of freedom in the early Universe. Thus, such limits typically focus on bosonic
particles such as the QCD axion, axion-like particles, Higgs-portal scalars,
and the dark photon. A powerful approach is to require new particle emission
to be subdominant to photon emission in stars [309, 310, 311, 312, 306],
analogous to the supernova bound wherein the new emission is limited by the
neutrino emission. If this rule were to be violated, stellar lifetimes would
be unacceptably short or other emission properties would change beyond
measured values. A different method of constraining light particle emission
from stars has been made possible recently by LIGO-Virgo Collaboration
observations of gravitational waves and the corresponding mass census enabled
by these observations, which are revealing the characteristics of Pop-III
stellar progenitors for the first time [313, 314]. One qualitative prediction
of Standard Model-only astrophysics is the existence of a “black hole mass
gap” formed from these objects at a characteristic mass scale slightly below
50 ${\rm M}_{\odot}$ [315, 316]. New particle emission, gravitational trapping
of dark matter, or dark matter coevolution all could change this mass scale
[317, 318, 319, 320, 321, 322]. Theory frontier activities in the stellar
domain promise to illuminate new, weakly-coupled particles that are not probed
by other mechanisms [323].

A different route by which dark matter could impact a “long-term” observable
of compact objects is via the formation of a super-radiant cloud that extracts
angular momentum from a central black hole [324, 325, 326, 327, 328]. For a
sufficiently low-mass dark matter particle, this could lead to detectable
changes in the observed black hole spin distribution [329, 330, 331, 332, 333,
334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348,
349, 350, 351, 352, 239, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362,
363, 364, 365, 366, 367, 368, 369]. Future theoretical explorations will lead
to a more comprehensive understanding of the impacts of backreaction of the
superradiance on the conditions necessary to support the superradiant
instability.

##  3 Dark Matter Origins and Structure Formation

Traditional methods of dark matter indirect detection are centered around the
idea of detecting the Standard Model byproducts of dark matter interactions
within astrophysical systems. New dark matter physics can also be indirectly
observed through its impact in the early Universe and on the subsequent
formation and evolution of collapsed structures of matter (see Fig. 3). Using
such detection methods can cover regions of dark matter parameter space that
are complementary to regions probed by traditional methods. Crucially,
gravitational indirect detection is necessary to probe certain classes of dark
matter theories that require the extreme conditions of the early Universe or
dark sector theories that have rich phenomenology but do not couple to known
physics except through gravity. In this section, we explore the theoretical
progress made in this area, often going hand-in-hand with advancements in
numerical simulations, and discuss the importance of continued theory efforts
to take full advantage of the influx of cosmological and astrophysical data
expected over the next decade.

Figure 3: Schematic representation of the coverage of current and future
probes of dark matter physics across various ranges of redshift $z$ (i.e.,
eras that observable photons or signals primarily originate from), wave number
$k$, and the corresponding halo mass $M_{\text{halo}}$. The ranges of
individual probes are approximate. Note that some of the listed probes are
well-established observationally, while some are still in nascent phases of
observational development, but they all represent complementary probes of dark
matter. We do not include probes that only affect background evolution and
thus do not have an associated scale $k$ to display in this figure. Similar
figures can be found in [e.g. 370, 371, 372].

###  3.1 Early-Universe Evolution

The present-day abundance of dark matter may have been established after a
period in which dark matter particles were in thermal and chemical equilibrium
with some larger thermal reservoir, or it may have been established despite
never attaining thermal equilibrium with its environment. The former case,
which we refer to as “thermal” dark matter, whether that thermal equilibrium
is attained with the Standard Model itself or with a secluded thermal bath, is
commonly considered to be UV-insensitive: the initial conditions of the dark
matter abundance will be erased by the thermal equilibrium condition. The
latter case of “non-thermal” dark matter leads to a large number of
observables that can potentially persist from the earliest moments of dark
matter genesis.

One exception to the rule that thermal dark matter is insensitive to early-
Universe microphysics could be if the dark sector underwent a first-order
phase transition. This could generate a gravitational wave signal [e.g. 373,
374, 375, 376, 377], which would remain thermally decoupled, even if dark
matter particles were in thermal equilibrium. In fact, the occurrence of the
first-order phase transition requires the dark sector to be at least self-
thermalised. The most widely studied example of this kind is a dark sector
Higgs mechanism, resulting in a phase transition that can be first order if
the sector contains a number of bosonic degrees of freedom [374]. Dark sector
confinement may also lead to the generation of a gravitational wave signal, if
the global symmetry is large enough at the time of breaking [e.g. 378, 379,
380, 381]. Such scenarios have been studied in the context of axion models
[380] and bound state formation such as dark quark nuggets [378]. Theoretical
progress is necessary before the gravitational wave phenomenology of first-
order phase transitions can be studied reliably: it has been demonstrated that
even in perturbative models, two-loop thermal effects must be included to
achieve better than $O(1)$ numerical accuracy [382, 383, 384]. Estimations of
the gravitational wave spectrum in non-perturbative hidden sector models have
used low- or high-energy effective field theories (see [379] for a
comparison), but their validity breaks down in the vicinity of the phase
transition. Future theory frontier efforts will be critical in understanding
this break down and extending the range of reliable predictions for models of
new physics.

Non-thermal dark matter may produce gravitational wave signals, but more
generally leads to a multitude of other tests of early-Universe physics. For
instance, the evolution of the post-inflationary axion can result in an
abundance of axion miniclusters [385, 386, 387, 388, 389, 390], which can
potentially be discovered with dedicated search strategies [391, 392, 393,
394, 395, 396, 397, 398]. Accurate predictions for the spectrum and abundance
of such miniclusters requires early-Universe simulations of the post-
inflationary axion, which are inherently difficult to perform due to a
separation of scales and large systematic uncertainties. Therefore, additional
large-scale simulations and systematic tests are needed in the future to
improve results.

Lastly, we note that the abundances of thermal and non-thermal dark matter are
both affected by the evolution of the Universe between the end of inflation
and the onset of Big Bang nucleosysthesis (BBN), and we cannot assume that the
Universe was radiation dominated throughout this period [399]. If dark matter
chemically decouples while the Universe is not radiation dominated, the larger
Hubble rate at a given temperature causes an earlier freeze-out and an
enhanced relic abundance [400, 401, 402, 403, 404]. If the subsequent
transition to radiation domination involves the creation of new Standard
Matter particles, as occurs after an early matter-dominated era, then the
relic abundance of dark matter is diluted [400, 405, 406, 407, 408]. An early
matter-dominated era also enhances dark matter density perturbations on scales
that enter the horizon prior to the onset of the final radiation-dominated
epoch [409]. Significant progress has been made in understanding the impact
this has on the abundance of sub-Earth-mass microhalos [409, 410] and how the
minimum halo mass depends on the properties of dark matter [411, 412, 413,
414], as well as the properties of the particle responsible for the early
matter-dominated era [415, 416, 417, 418]. These microhalos provide a new
observational probe of the early Universe; their impact on the dark matter
annihilation rate can be constrained using the isotropic gamma-ray background
[413, 415, 419], and they can be detected gravitationally using pulsar timing
arrays [420, 421, 422, 423] and observations of stellar microlensing events in
galaxy clusters [424, 425]. Further study is needed to understand whether the
CMB and the 21cm background could further constrain dark matter annihilation
in early-forming microhalos.

###  3.2 Early-Universe Structure Formation

The standard cosmological model of $\Lambda$CDM describes the large-scale
structure of the Universe extremely well. The presence of CDM is crucial
through its contribution to the overall energy density and through its density
perturbations at early times. Comprising about 84% of the matter content in
the Universe [426], the gravitational influence of dark matter is key in the
formation of structure. Thus, cosmological observations provide important and
unique insight into new dark matter physics that disturb the predictions of
CDM.

Light degrees of freedom: A wide variety of dark matter models introduce new
light degrees of freedom in the Universe at early times. In particular, dark
sectors may contain light or massless force carriers, such as dark photons,
that thermalize dark matter at a temperature that generally differs from the
Standard Model bath. The introduction of new relativistic species alters the
expansion rate of the Universe during radiation domination, in turn affecting
CMB anisotropies [e.g. 427] and predictions of the abundances of light
elements created during BBN [e.g. 428, 429]. Standard contributions to the
energy density of radiation during the BBN and CMB eras include photons and
neutrinos, assuming their masses are not too large; however, neutrinos
decouple from the photon bath at temperatures $\sim 1~{}\mathrm{MeV}$, and
their energy density contribution is encoded in the parameter
$N_{\mathrm{eff}}$. For the three active neutrinos of the Standard Model,
recent calculations yield $N_{\mathrm{eff}}^{\mathrm{SM}}=3.044$ [430, 431,
432, 433], and deviations $\Delta N_{\mathrm{eff}}\equiv
N_{\mathrm{eff}}-N_{\mathrm{eff}}^{\mathrm{SM}}$ from this value could imply
the existence of non-standard physics. Current CMB and BBN observations
constrain $N_{\mathrm{eff}}$ to be close to its Standard Model value [e.g.
426]; therefore, in order to incorporate new massless species in a
cosmological model, the dark sector temperature has to be lower than that of
the photon bath to avoid contributing too much to the relativistic energy
budget.

Thermal dark matter itself can contribute to the relativistic energy density
during BBN if its mass is $\lesssim 20~{}\mathrm{MeV}$. Additionally, if the
dark matter relic abundance is set through a standard freeze-out process, dark
matter may annihilate into neutrinos or visible particles, which in turn alter
weak interaction rates that determine primordial abundances. Dark matter
coupled to neutrinos or charged particles generates a positive or negative
contribution, respectively, to $N_{\mathrm{eff}}$. Thus, cosmological
observations can provide robust bounds on the mass of dark matter, for a given
spin and annihilation channel [434, 435, 436, 435, 437, 438, 439]. In the
future, CMB-S4 will obtain a sensitivity to new thermalized, light relics
corresponding to $\Delta N_{\mathrm{eff}}<0.06$ at $2\sigma$ [440]. Dedicated
theory work will be needed to understand the implications of CMB and BBN
constraints across a variety of dark sector models.

CMB spectral distortions: Measurements of the CMB energy spectrum provide an
opportunity to search for new physics that impacts the thermal history of the
Universe. Deviations of the CMB spectrum from a perfect blackbody, referred to
as spectral distortions, are sensitive to processes that inject energy into
(or extract energy from) the photon-baryon plasma at redshifts $z\lesssim
2\times 10^{6}$. Current measurements of the CMB spectrum show that it is
extremely close to a blackbody with a present-day temperature
$T_{0}=2.72548\pm 0.00057~{}\mathrm{K}$ [441, 442], with spectral distortions
smaller than a few parts in $10^{5}$ [441]. Proposed experimental concepts
could probe spectral distortions at least three orders of magnitude smaller
[443], thus opening new windows into exotic physics in the early Universe.
Several known processes within the standard $\Lambda$CDM cosmological model
generate spectral distortions [444]. In addition, spectral distortions may be
generated through dark matter interactions with Standard Model particles.

Dark matter annihilating or decaying into photons or electrically charged
particles would inject energy into the photon-baryon plasma, hence distorting
the CMB energy spectrum [445]. CMB anisotropies are significantly more
sensitive to $s$-wave annihilations than spectral distortions [445]; however,
spectral distortions could be more sensitive to $p$-wave annihilations [446],
depending on the specifics of the dark matter model. In addition, spectral
distortions can constrain decaying particles with lifetimes
$10^{6}~{}\textrm{sec}\lesssim\tau\lesssim 10^{12}~{}\textrm{sec}$, to which
CMB anisotropies are insensitive. For such short lifetimes, the decaying
particle could only comprise a small fraction of the total dark matter
abundance [447].

Alternatively, dark matter particles may _extract_ energy from the photon-
baryon plasma if they scatter elastically with photons, electrons, or nuclei
[448, 446]. Indeed, if dark matter is heavier than $\sim 1$ keV, it is non-
relativistic by $z\sim 2\times 10^{6}$ and therefore cools down adiabatically
faster than the thermalized photon-baryon plasma. Elastic scattering would
therefore lead to a systematic transfer of heat from the plasma to the dark
matter fluid. This effect is increasingly large for light, thus more abundant,
dark matter particles. While current spectral distortion limits only constrain
elastically-scattering dark matter particles with masses $m_{\chi}\lesssim
100$ keV, proposed experiments could extend this sensitivity to $\sim$ GeV
masses. Continued theoretical work is needed to ensure robust predictions
[e.g. 449].

CMB anisotropies and dark matter annihilation/decay: Dark matter annihilation
or decay via electomagnetic channels injects energy into the photon-baryon
plasma, which increases the free-electron fraction $x_{e}$ around and after
cosmological recombination at $z\lesssim 1100$. The increase in $x_{e}$ delays
the last scattering epoch and affects the photon diffusion scale (and hence
the damping of CMB anisotropies at small scales). Additionally, an increased
$x_{e}$ in the low-redshift tail of recombination suppresses CMB anisotropies
on small scales and increases large-scale polarization fluctuations, an effect
qualitatively similar to an increase in the reionization optical depth [450].

Through these effects, CMB anisotropies are sensitive to very rare dark matter
annihilation or decay processes [451, 212], since as little energy as $\sim 1$
eV per baryon suffices to significantly alter the ionization history. In
particular, even for dark matter produced in a standard freeze-out scenario,
residual annihilation at $z\lesssim 1100$ may have a significant impact on CMB
anisotropies, long after they no longer change the dark matter abundance.
_Planck_ data constrain the dark matter $s$-wave annihilation cross section to
$\langle\sigma v\rangle\lesssim 3\times 10^{-28}(m_{\chi}/\textrm{GeV})$,
ruling out a standard freeze-out production of dark matter for
$m_{\chi}\lesssim 10$ GeV [7]. _Planck_ data also constrain the lifetime of
decaying dark matter to $\tau\gtrsim 10^{24}$–$10^{25}$ sec, depending on the
decay channel [452, 453], orders of magnitude larger than the age of the
Universe. Near-future and planned CMB-anisotropy missions could achieve a
factor of $\sim 30$ improvement in the sensitivity over current Planck limits
on dark matter annihilation and decay [454].

More exotic dark matter candidates, such as PHBs, can be probed by CMB
anisotropies through similar effects. PBHs can inject energy in the photon-
baryon plasma through either Hawking radiation for masses $M\lesssim 10^{17}$
g [453] or accretion-powered radiation for masses $M\gtrsim M_{\odot}$ [455,
456, 457]. In contrast with the rather clean and well-understood physics
involved in dark matter annihilation or decay [212, 458], the complex physics
of accretion is highly uncertain and much theory work remains to be done to
make existing limits more robust.

While the effects described above arise from changes to the _average_ free-
electron fraction, inhomogeneous energy injection from dark matter would also
lead to spatial fluctuations in $x_{e}$ [459, 460]. These fluctuations would
induce non-Gaussianities in CMB anisotropies, which could be a complementary
avenue to probe energy injection from dark matter.

CMB anisotropies and dark matter scattering: Elastic scattering between dark
matter and Standard Model particles in the early Universe can alter the
evolution of perturbations, impacting CMB temperature, polarization, and
lensing anisotropies. Scattering processes heat the dark matter fluid and
induce a drag force from the exchange of momentum. The primary effect of the
scattering is inhibiting the clustering capabilities of dark matter, thus
washing out structure on a variety of observable scales. As a result, the CMB
power spectra experience damping at large multipoles $\ell$, corresponding to
small angular scales on the sky, for models where dark matter decouples from
baryons prior to matter-radiation equality [461, 462, 463, 464, 465, 466,
467]. For models such as millicharged dark matter, scattering takes place at
later times, and CMB anisotropy currently provides some of the best
observational bounds on such models [e.g. 464, 468, 469]. The theoretical
developments and numerical implementation into Boltzmann codes, such as CAMB
and CLASS, have enabled CMB searches of dark matter scattering with baryons
[461, 462, 463, 464, 465, 466, 467], electrons [470, 471], photons [472, 473,
474], and neutrinos [475, 476]. The strength of the interaction is a key
parameter that controls the amount of power suppression in the CMB primary
anisotropy, but including an energy or velocity dependence of the interaction
influences the shape of the suppression, potentially allowing a way to
distinguish between various scattering models. Even in the case of dark
sectors, dark matter scattering with dark radiation [477, 478, 479] produces
features in the CMB power spectra that can be differentiated from other models
[480]. Changing $N_{\mathrm{eff}}$ can have a similar effect of suppressing
the CMB damping tail, but possible degeneracies can be broken using CMB
lensing anisotropies [481].

Upcoming ground-based instruments, such as the Simons Observatory [482] and
CMB-S4 [440], will measure the CMB with better precision at high $\ell$ and a
much higher angular resolution than current experiments, allowing for greater
sensitivity to dark matter interactions. In terms of theoretical development,
most investigations have focused on thermal relic models, while future
investigations of models where dark matter is produced non-thermally will also
be of high interest in context of CMB probes. Furthermore, there is a notable
synergy between the CMB primary anisotropy and other probes of the structure
growth in the Universe, which can be further exploited in self-consistent
analyses of CMB with other observables, for specific dark matter models.

21-cm line at high redshifts: The redshifted 21-cm line of neutral hydrogen
presents a unique probe of the post-recombination Universe, prior to the birth
of the first stars (cosmic dark ages, $z=30$–$100$) and right after it (cosmic
dawn, $z=5$–$30$)—see [e.g. 483, 484] for reviews. The corresponding
absorption signal imprinted on the CMB backlight during cosmic dawn [485]
captures the state of hydrogen gas and various microphysical processes that
control it at this early epoch; mapping the absorption signal provides a (3D)
view of the Universe at epochs that no other probes can reach. Many dark
matter processes can affect the temperature of baryons during cosmic dawn, in
turn affecting the 21-cm signal. The experiments targeting this era can use
this connection to probe dark matter interactions with the visible sector.

A well-motivated model that can affect the 21-cm signal involves dark matter
scattering with baryons through a light mediator [486, 487, 488, 489, 490,
466, 468, 491, 492]. For millicharged dark matter, current 21-cm measurements
(e.g., from EDGES in the global signal [493] or HERA for fluctuations [494])
exclude millicharges as low as $q_{\chi}\sim 10^{-6}\,e$ [488] (where $e$ is
the electron charge), even if less than a percent of dark matter is
millicharged. Alternatively, models of dark photons that kinetically mix with
Standard Model photons, with mixing parameter $\epsilon\sim 10^{-7}$ [495],
can create a radio background that affects the 21-cm signal [495, 496, 497].
Additionally, a classical WIMP, for instance, can heat gas through
annihilations [498, 499], and similar effects occur in case of decaying dark
matter and dark-photon dark matter [500, 501]; each in turn can affect the
thermal properties of baryons during cosmic dawn. Even more exotic models,
such as evaporating or accreting PBHs, can produce heating [502, 503].

The 21-cm signal during cosmic dawn is sensitive to structure formation
because the first galaxies emit photons that produce Wouthuysen-Field coupling
[485], critical for the 21-cm absorption feature to arise. Those first
galaxies were hosted in halos with masses $\sim 10^{6}\,M_{\odot}$ [504, 505,
506, 507], which correspond to fluctuations with wavenumbers as large as
$k\approx 100$–$200\,\rm Mpc^{-1}$. As a consequence, altering the
corresponding scales in the linear matter power spectrum affects the abundance
of the first galaxies and the timing of the 21-cm signal [508]. Small scales
are often very sensitive to dark matter microphysics and can be used to probe
warm dark matter and other beyond–CDM models.

While there are claims that the global (sky-averaged) signal has already been
detected [493], the tomographic signal is yet to be measured [494] from
interferometers such as HERA [509], LOFAR, MWA, or SKA [510]. However, it is
expected that these observatories can yield constraints on the matter power
spectrum up to $k=100\,\rm Mpc^{-1}$ at the $\sim 10\%$ level [508], which can
place powerful constraints on specific dark matter candidates such as ETHOS
models [511], warm dark matter [512], or fuzzy dark matter [513].

High-redshift galaxy luminosity function: The luminosity function (i.e.,
counting the number of galaxies versus their luminosity) provides a tracer of
the abundance of dark matter halos at the redshifts of measurement. UV
luminosity functions are constructed from the HST Ultra Deep Fields (HUDF),
where the UV light from the most massive galaxies at $z=4$–$10$ is detected by
the visible/IR filters at the HST [514, 515]. JWST observations will
significantly contribute to constraining the population of early galaxies in
the coming decade. There measurements can be used to determine the matter
power spectrum during reionization up to $k=10\,\rm Mpc^{-1}$ [372, 516, 517]
and can provide probes of warm dark matter [518, 519, 520, 521], fuzzy dark
matter [522, 523], and ETHOS models [524].

Lyman-$\alpha$ forest: The clustering of matter at intermediate redshifts
traced by the redshifted forest of Lyman-$\alpha$ absorption lines is a
sensitive probe of dark matter physics. Several authors have forward-modeled
the Lyman-$\alpha$ forest to place lower limits on the thermal relic warm dark
matter mass of $\mathcal{O}(3$–$5)\ \mathrm{keV}$ [525, 526, 527, 528], where
the details of the constraints depend on astrophysical assumptions about the
temperature, density, and redshift evolution of baryons in the intergalactic
medium [529, 530]. Other dark matter models such as those with dark
matter–baryon interactions, ultra-light axions, and PBHs have also been
constrained using similar methods [531, 532, 533, 534], although there are
dark matter-related modeling challenges in some cases [e.g. 535]. From a
theoretical standpoint, the development of Lyman-$\alpha$ forest emulators
[e.g. 536] has contributed to recent advances and will become increasingly
important to enable robust, joint inference of cosmological, astrophysical,
and dark matter physics in the coming decade. From an observational
standpoint, dark matter analyses have generally been performed using $\sim
10$s of high-resolution spectra (e.g., VLT, HIRES/KECK; [525]), $\sim 100$s of
intermediate-resolution spectra (e.g., XQ-100; [527]), or $\sim 1000$s of low-
resolution spectra (e.g., SDSS/BOSS; [528]). Ongoing spectroscopic surveys
including DESI will significantly enhance the number and redshift coverage of
available high-resolution quasar spectra, potentially allowing for percent-
level measurements of the Lyman-$\alpha$ flux power spectrum on small scales
[537].

###  3.3 Present-Day Structure

Probes of small-scale structure at low redshifts have recently emerged as a
key means to test a variety of dark matter properties, including its
production mechanism, primordial temperature, self- and Standard Model-
interactions, and minimum particle mass. These probes can broadly be
categorized according to whether they rely on observations of the baryonic
contents of low-mass halos or not. Here, we summarize the current status and
future prospects for each of these probes, along with key theoretical
considerations. In particular, we emphasize that connecting theoretically
motivated predictions for dark matter’s gravitational imprints to precise
analytic and simulation-based predictions for small-scale structure
distributions is a critical area for work over the next decade.

Massive galaxy clusters provide a unique opportunity to stringently test the
CDM paradigm of structure formation. Combining strong and weak gravitational
lensing detected in high-resolution images of massive clusters has revealed
that the dark matter subhalos of cluster galaxies are less massive and less
spatially extended compared to those hosting equivalent luminosity field
galaxies, indicating that tidal stripping of dark matter is efficient in these
dense, violent environments—see review by [538] and, for a critical analysis
of the range of lens modeling methodologies, see [539] and [540] for recent
developments. Comparison of the derived subhalo mass function from observed
cluster lenses with CDM simulations has revealed that while the abundance and
mass function of substructures was well reproduced, the radial distribution of
subhalos was discrepant [541]. Subhalos are more concentrated in the inner
regions of observed clusters than predicted by CDM simulations.

A recent study of Galaxy-Galaxy Strong Lensing (GGSL) in clusters found that
observed small-scale cluster substructures (on $\sim 5$–$10$ kpc scales) are
more efficient strong lenses than predicted by CDM simulations by more than an
order of magnitude [542]. Further theoretical investigation will be needed to
evaluate if this large discrepancy arises from hitherto undiagnosed systematic
issues within simulations, or if in fact this serves as a hint for deviations
from the CDM paradigm. Numerical effects arising from the resolution limits of
simulations that lead to artificial subhalo disruption [543] cannot account
for the order of magnitude GGSL gap, as they are at most a 20% effect [544].
Importantly, baryonic feedback processes must be carefully investigated as a
potential culprit for the discrepancy, as it is well understood that they
alter the internal structure of cluster galaxies. This motivates a comparison
of simulated galaxy clusters across several independent CDM simulations.

The GGSL discrepancy could potentially be revealing that dark matter might not
be collisionless, especially in the extremely dense cluster environments. For
elastic self-interactions that are velocity dependent (with large interaction
cross sections), halos can undergo gravo-thermal collapse just as stellar
systems. When this occurs, the inner halo develops a negative heat capacity
due to outward transfer of energy [545], resulting in a significant
enhancement of the concentration of the inner density profile—precisely in the
direction needed to address the GGSL discrepancy [546]. The transformation
produced by core-collapse motivates the investigation of this particular class
of self-interacting models more deeply. Moreover, totally inelastic self-
interactions can result in a collapse time-scale up to two orders of magnitude
shorter than for the elastic case [547], for smaller interaction cross
sections. Further theoretical study is needed to map out the space of self-
interacting dark matter models that can potentially account for the GGSL
discrepancy.

Dwarf galaxies are the smallest dark matter-dominated baryonic systems in the
Universe and form in halos with $M_{\mathrm{halo}}\lesssim 10^{10}\
M_{\mathrm{\odot}}$, down to the galaxy formation threshold of
$M_{\mathrm{halo}}\sim 10^{8}\ M_{\mathrm{\odot}}$ [548, 549]. Thus, the
smallest “ultra-faint” dwarf galaxies [550] are a particularly sensitive probe
of low-mass halo abundances, which reflect dark matter’s small-scale
gravitational clustering. To date, ultra-faints have exclusively been detected
within the virial radius of the Milky Way as satellite galaxies; recent wide-
field photometric surveys, including the Sloan Digital Sky Survey, Pan-
STARRS1, and the Dark Energy Survey, have increased the number of known Milky
Way satellites to roughly $60$ systems (see [551] for a recent census of the
Milky Way satellite population). These observations have been used to
constrain the warm dark matter particle mass at the level of $6.5\
\mathrm{keV}$, the particle mass of fuzzy dark matter at the level of
$2.9\times 10^{-21}\ \mathrm{eV}$, and the dark matter–proton interaction
cross section at the level of $10^{-29}\ \mathrm{cm}^{2}$ [552] (also see
[548, 553, 554, 555, 556, 557]). Over the next decade, observational
facilities, including the Vera C. Rubin Observatory and the Nancy Grace Roman
Space Telescope, are expected to significantly improve upon current dwarf
galaxy discovery power, both within and well beyond the virial radius of the
Milky Way [e.g. 558, 559]. With these upcoming improvements, continued
theoretical developments are key to properly interpreting possible deviations
of halo abundances from the CDM expectation.

In addition to their mass abundances, the individual properties and population
statistics of dwarf galaxies are also sensitive to dark matter microphysics.
For example, dark matter self-interactions can both suppress the inner
densities of halos in a mass-dependent fashion [560, 561, 562, 563, 564] and
eventually drive these systems towards gravothermal core collapse [545, 565,
566, 567, 568, 569, 570, 571, 572]. These effects provide a mechanism for
explaining the observed diversity of galactic rotation curves [573, 574, 575,
576], although current observations are not yet sufficient to distinguish this
scenario from feedback-affected CDM halos [577]. Conservative constraints
based on the observed inner-most densities of dwarf galaxies such as Draco
[e.g. 578], coupled with constraints from galaxy clusters [e.g. 579],
demonstrate that self-interacting dark matter models with velocity-dependent
interactions must undergo some degree of gravothermal collapse [580]. This
observation may provide a mechanism to explain observations suggesting that
the most centrally-dense Milky Way dwarfs also have the smallest orbital
pericenters [581]. Improved theoretical modeling of dwarf properties and
populations will be needed to harness the full potential of current and
upcoming surveys that are amassing information on dwarf galaxies of Milky Way-
like systems [582, 583], as well as improved stellar kinematic data on the
Milky Way’s dwarfs from observatories like _Gaia_ [584].

Strong gravitational lensing allows us to detect low-mass halos within lens
galaxies and along the line of sight via their effect on the observed multiple
images of a background source. This process is purely gravitational and
independent of whether these low-mass halos contain any baryons. It thus
provides a unique approach to test dark matter models by probing the low-mass
end of the halo and subhalo mass functions beyond the local Universe. The
detection of low-mass halos with strongly lensed quasars is mainly based on
so-called flux ratio anomalies—that is, changes induced to the relative flux
of the multiple images [e.g. 585, 586, 587]. In images of strongly lensed
galaxies, a local change of the surface brightness distribution of the data,
reflecting a change in the relative position of the images, is the tell-tale
signature of the presence of low-mass halos [e.g. 588, 589, 590, 591, 592].
This method is often referred to as the gravitational imaging technique.

Flux ratio anomalies and the gravitational imaging technique are complementary
approaches that are subject to individual and shared sources of systematic
errors [593, 594]. The two techniques can also differ in their sensitivity to
low-mass haloes. Depending on the size of the background source, flux ratio
anomalies typically probe the halo and subhalo mass functions down to masses
as low as $\sim 10^{7}\ M_{\mathrm{\odot}}$ and potentially below. The number
of available lens systems and the precision of the flux measurement then set
the precision with which one can constrain the halo and subhalo mass functions
[595]. For example, [596] and [593] constrain the warm dark matter particle
mass at 5.2 (5.5) keV at the $95\%$ confidence level using eight (seven)
quadruply imaged quasars.

The sensitivity to low-mass halos reached by the gravitational imaging
technique is highly dependent on the angular resolution of the observations
[597]. At present, only a handful of systems for which Very Long Baseline
Interferometry observations are available can probe the halo mass function
down to $\sim 10^{6}\ M_{\mathrm{\odot}}$ [598]. From a sample of 20 HST-
observed galaxy-galaxy lensed systems (sensitivity $\sim
10^{10}M_{\mathrm{\odot}}$), [594] infer a limit on the warm dark matter
particle mass of $1.02~{}\mathrm{keV}$ using both detections [599] and non-
detections [600, 601].

At present, the relatively low number of gravitational lens systems with high-
enough data quality significantly limits the constraints on dark matter from
both flux-ratio anomalies and the gravitational imaging technique. Luckily,
ongoing and future surveys with instruments such as Euclid, the Vera Rubin,
and SKA will increase the number of known gravitational lens systems by
several orders of magnitudes [602, 603, 604]. This data, coupled with follow-
up observations with, e.g., the ELT, TMT, and JWST, is projected to deliver
tight constraints on the halo and subhalo mass function [595, 605].

Stellar streams are the tidally disrupted remnants of dwarf galaxies and
globular clusters. Recently, the combination of astrometric, photometric, and
spectroscopic observations has led to the discovery of a plethora of new
streams orbiting the Milky Way [606, 607, 608] and intriguing structure in the
density profiles of nearby streams like GD-1 [609] and ATLAS–Aliqa Uma [610].
These substructured streams—and particularly the gaps in stream density
profiles and other unexpected, off-stream features—have been modeled to place
constraints on the properties of individual perturbers and candidate dark
matter subhalos that may have gravitationally perturbed these streams [611],
as well as the population statistics of subhalo perturbers in cold and warm
dark matter contexts [612, 613]. Deeper photometric measurements from upcoming
facilities will continue to increase the population of known streams and
reveal their fine-grained density structure, with potential sensitivity to
subhalos as small as $\sim 10^{6}\ M_{\mathrm{\odot}}$, regardless of their
baryonic content [614, 559].

##  4 Machine Learning and Statistics

Figure 4: Simplified comparison of likelihood-based and simulation-based
algorithms in the space of number of required/affordable simulations vs.
number of model parameters (including parameters of interests, uncertain
parameters, and random states of the simulator). In general, the simulation
requirements of likelihood-based techniques grows significantly with the
number of model parameters. Instead, simulation-based inference techniques
can—in principle—directly focus on estimating marginal posteriors for
parameters of interest, independently of the total number of parameters. This
reduces the need for parameter reduction techniques and enables the comparison
of complex simulation results with complex data.

Over the next decade, astrophysical data relevant for the study of the nature
of dark matter will increase not only in volume, but also in complexity and
detail. Upcoming gamma-ray and radio observatories like the Cherenkov
Telescope Array (CTA) [37] and the Square Kilometer Array (SKA) [615, 616]
will produce petabytes of data [55]. Fully exploiting this data for scientific
purposes will require increasingly detailed and complex physical models, which
bring along higher computational costs for simulations, as well as a larger
number of uncertain parameters, including those characterizing signal and
background systematics. Established algorithms for parameter inference, like
Markov Chain Monte Carlo (MCMC), nested sampling [617, 618], and Approximate
Bayesian Computation (ABC) often require a very large number of simulation
runs, which often grow significantly as the number of model parameters
increases; see Fig. 4 for an illustration. In many settings, it becomes
impractical to compare physical models in their full complexity and detail
with the data. As a result, analyses are often limited by the inference tools
rather than statistics [619, 620]. Modern statistical algorithms based on deep
learning and differentiable programming techniques can overcome the
limitations of established techniques. Recent reviews can be found in [621,
622, 619], and we will provide a brief overview of promising techniques and
suggest necessary developments here.

Scalable inference techniques: Stochastic variational inference (SVI) [623,
624] approaches inference of the posterior as an optimization problem,
circumventing the need to sample from high-dimensional parameter spaces. The
most commonly employed optimization target is here the evidence lower bound
(ELBO) [623]. It can be conveniently optimized using stochastic gradient
descent (SGD), provided the physical simulator is fully differentiable with
respect to all model parameters. This approach can scale to very high
dimensional inference problems. Example applications are deblending starfields
[625], disentangling the components of gamma-ray emission [626, 627], and
strong gravitational lensing [628, 629]. One challenge with SVI is that
through the mode-seeking nature of the reverse KL divergence [630], it tends
to underestimate the posterior variance, potentially leading to over-confident
posteriors. An important theoretical development front is the construction of
differentiable forward models and simulators [e.g. 631, 632], which is easily
admitted using modern automatic differentiation tools [633, 634], or the use
of differentiable surrogate models when this is not feasible [635, 636].

The use of differentiable models also allow for inference via gradient-
assisted Monte Carlo methods like Hamiltonian Monte Carlo, which have higher
sample efficiency and scale better with parameter dimension than traditional
Monte Carlo techniques.

Methods based on deep learning: The likelihood function, which is a
fundamental input to most established techniques including SVI, can be
extremely difficult to compute, due to required marginalization over various
unobserved instrumental and physical parameters (see Fig. 4 for an
illustration). Simulation-based inference (SBI) methods (see [637, 638])
circumvent the evaluation of likelihoods by directly mapping observations and
simulations onto summary statistics that are subsequently statistically
interpreted. A classical SBI technique is ABC [639]. Various recently
developed neural SBI methods use the training of deep neural networks both to
generate informative summary statistics as well as performing estimation of
posteriors, likelihoods [e.g. 640, 641], or likelihood-to-evidence ratios
[e.g. 642]. This procedure can require orders of magnitude fewer simulations
than established techniques [643, 644], see Fig. 4. Neural SBI has been used,
for instance, for dark matter substructure inference [645, 628, 646, 647],
dark matter indirect detection with gamma-ray data [648, 649, 650], and binary
microlensing [651]. Fronts where still significant theoretical development is
required are neural network architectures tailored to the structure of typical
astrophysical data, which can significantly reduce simulation costs for
simulation-based algorithms, and simulation-efficient training algorithms.
This includes, for example, efforts to develop interpretable and/or
explainable architectures for astrophysical data processing and the use of
inference algorithms that produce statistically sound results for the purposes
of scientific discovery and hypothesis testing [652]. These developments will
also help foster community trust in results relying on deep learning methods,
which have historically seen reluctance in adoption due to their reputation as
black boxes.

In general, deep learning-based techniques enable more information to be
extracted from data without requiring the use of simplified data
representations and low-dimensional summary observables. Although this has the
potential to significantly enhance the sensitivity of astrophysical dark
matter searches, it can make typical methods more sensitive to how specific
features in the data are modeled. This underscores the need for increased
attention to accurately modeling the data.

Infrastructure and workforce: Realizing these goals will require development
of both software and human resources. Given the potentially steep theoretical
learning curve associated with the aforementioned statistical methods, the
development of easy-to-use inference tools [e.g. 644, 653] adopting good
documentation practices with end practitioners in mind is crucial.

Finally, given the necessity of cross-disciplinary expertise in developing
these methods and tools, we recommend, through appropriate hiring practices
and promotion options, viable career trajectories at the intersection of
statistical methods and astrophysical data analysis for new physics. A
concerted effort in this direction has demonstrated success in certain fields
of cosmological [654] and collider [655] data analysis. At the training stage,
the existence of Ph.D. schools as well as curriculum-based learning of data
analysis techniques is encouraged.

##  5 Conclusions

We are entering an era which holds the promise of resolving many of the most
basic questions we have about dark matter. How was dark matter produced in the
early Universe? Is dark matter a single missing piece or part of a broader
dark sector? Is dark matter cold, warm, or better thought of as a wave? And
above all else: what is dark matter?

A central source for optimism that the answer to these questions may be within
our grasp is the upcoming advancements in instruments and observations. Yet,
as we have outlined, the role of the theory community is not to simply wait
for the experimental program to provide the answers to these questions, but
instead to work with, extend, and optimize dark matter searches. Indeed, there
is considerable work ahead for theorists to determine the behavior of dark
matter and how this would manifest in our observations, and further in the
development of techniques such as machine learning that could be required to
confidently detect an eventual signal. While there are many challenges to
overcome, as we have reviewed, there are clear paths for doing so. Viewed as a
whole, there is every reason to be confident that in the coming years we will
finally tease apart the mysteries of dark matter and move into a future where
rather than wondering what dark matter is, we are instead asking how its
particle nature modifies galaxies, cosmology, and possibly even opens a path
towards understanding the broader world of physics that exists beyond the
Standard Model.

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