The observational tension between the large-scale cosmic structure predicted by Cold Dark Matter (CDM) simulations and the actual observed distribution of galaxies has significant implications for the nature of dark matter. The discrepancies observed at small scales—such as the mismatch between the predicted and observed number of satellite galaxies, as well as the core-cusp problem—have prompted reconsideration of the standard CDM paradigm and the exploration of alternative dark matter models. The findings from Lyman-alpha forest data and galaxy surveys are critical in constraining various dark matter candidates like sterile neutrinos and axions. The interplay between dark matter properties and the early universe dynamics could help resolve some of the observed anomalies, offering a path beyond the standard CDM model.

Implications of Discrepancies for the Nature of Dark Matter

1. Core-Cusp Problem and Small-Scale Anomalies
   • The core-cusp problem refers to the discrepancy between the predicted dense central cusps in dark matter halos (as per CDM simulations) and the observed flatter cores in certain galaxies (particularly dwarf galaxies). Additionally, the too many satellite galaxies problem involves predictions from CDM simulations that galaxies should have more satellite galaxies than observed.
   • These small-scale observations suggest that dark matter may not behave exactly as predicted by the standard cold dark matter model. In particular, it implies that dark matter could possess properties that lead to more smoothly distributed halos (i.e., cores instead of cusps), and fewer satellite galaxies may be able to form due to interactions within the dark matter.
2. Hints Toward Alternative Dark Matter Models
   • These discrepancies encourage the exploration of non-CDM dark matter models, which include candidates like self-interacting dark matter (SIDM), sterile neutrinos, and axions.
   • SIDM posits that dark matter particles interact with each other through a force other than gravity, which would lead to redistribution of dark matter within halos and potentially resolve the core-cusp problem. However, the correct amount of self-interaction is still under investigation.
   • Sterile neutrinos and axions are light dark matter candidates with different particle physics properties that could also resolve some of the issues seen in CDM.

Constraining Dark Matter Candidates with Lyman-Alpha Forest and Galaxy Surveys

1. Lyman-Alpha Forest:
   • The Lyman-alpha forest refers to a series of absorption lines observed in the spectra of distant quasars, caused by hydrogen gas in the intergalactic medium. These absorption lines can be used to map the distribution of matter in the universe, including dark matter, by looking at the small-scale density fluctuations at high redshifts.
   • Lyman-alpha forest data are sensitive to the distribution of matter at small scales and can be used to place tight constraints on dark matter models, especially regarding the free-streaming properties of dark matter.
   • In particular, hot dark matter candidates like sterile neutrinos or warm dark matter (such as axions) would have different free-streaming lengths compared to cold dark matter, and this would lead to observable differences in the small-scale power spectrum of matter distribution. These observations help rule out certain classes of sterile neutrinos and axions that do not match the observed data.
2. Galaxy Surveys:
   • Large galaxy surveys, such as SDSS (Sloan Digital Sky Survey) and future surveys like EUCLID, provide information about the large-scale structure of the universe (galaxy clusters, voids, and cosmic web), which is influenced by the underlying dark matter distribution.
   • These surveys help in measuring galaxy clustering, void distribution, and galaxy-halo connections, which are sensitive to the dark matter model. The observed distribution of galaxies on these scales helps constrain the behavior of dark matter by comparing simulations that include different dark matter candidates.
   • Axions, for example, are expected to be much lighter than CDM particles and would affect the growth of structure in a different way, suppressing the formation of small-scale structures. If axions are confirmed as the dominant form of dark matter, they would likely lead to a lack of small-scale power in galaxy surveys, consistent with the absence of small galaxies predicted by CDM.

Early Universe Dynamics and Dark Matter Properties

The early universe dynamics play a crucial role in shaping the behavior of dark matter, especially in terms of its influence on structure formation. The thermal history of the universe, which includes the decoupling of dark matter from the photon-baryon fluid, sets the initial conditions for how dark matter clusters and interacts in the post-recombination era. The interplay between dark matter properties and these early dynamics could help resolve some anomalies that arise within the CDM paradigm.

1. The Impact of Dark Matter Properties:
   • The free-streaming length of dark matter particles is crucial in determining the scale of structures that form in the early universe. Warm dark matter (such as axions or sterile neutrinos) would have a larger free-streaming length than cold dark matter, leading to a suppression of small-scale structure formation and fewer small halos (as observed).
   • The decoupling of dark matter from the standard model particles (through processes like reheating and decay of dark matter) sets the stage for the growth of structure. Dark matter models that interact more or less efficiently can have different effects on this early phase of cosmic history, influencing both the formation of large-scale structures and the small-scale power that we observe today.
2. The Role of Interactions and Decoupling:
   • Sterile neutrinos, for instance, could decouple from the thermal bath earlier than CDM and could produce a “hotter” universe at smaller scales, leading to the suppression of small-scale structure, potentially explaining the observed paucity of satellites around large galaxies.
   • Axions also behave as ultra-light bosons, and their interactions (or lack thereof) could lead to a very different phase transition in the early universe compared to CDM, with potentially enhanced clustering at larger scales but reduced clustering at small scales.

The discrepancies between the large-scale cosmic structure predicted by CDM and the observed distribution of galaxies challenge our understanding of dark matter and its properties. Observations from the Lyman-alpha forest and galaxy surveys are critical in constraining various dark matter candidates, such as sterile neutrinos and axions, and they provide strong evidence for the behavior of dark matter on small scales.

The interplay between dark matter properties and early universe dynamics offers a promising path to resolving these anomalies. By extending beyond the standard CDM paradigm, models like self-interacting dark matter (SIDM), sterile neutrinos, and axions provide different frameworks for understanding the formation of cosmic structures. Future observations, especially from EUCLID and other large surveys, will likely provide the key insights needed to refine or revise our models of dark matter and its role in the evolution of the universe.

The latest observations of the Cosmic Microwave Background (CMB) anisotropies, along with Baryon Acoustic Oscillations (BAO) and weak lensing surveys, provide powerful insights into the properties of dark matter and its role in the early universe. These observations allow for the precise measurement of the universe’s expansion rate, structure formation, and the evolution of matter and radiation, placing significant constraints on the interactions, thermal relic density, and nature of dark matter. The potential existence of exotic dark matter candidates such as dark photons, ultra-light scalar fields, and primordial black holes introduces alternative models that could challenge or expand our understanding of dark matter. Here’s how these observations help refine our understanding of dark matter’s properties and its connection to cosmic inflation and the formation of the first structures:

1. CMB Anisotropies and Dark Matter

• The CMB provides a snapshot of the universe at approximately 380,000 years after the Big Bang, offering critical information about the distribution of matter, radiation, and the underlying physics governing cosmic expansion. The anisotropies (tiny temperature fluctuations) in the CMB arise from the interactions between photons and baryons before recombination.
• Dark matter influences the formation of these anisotropies through its gravitational effects. Its density and clustering properties impact the sound waves in the early universe’s plasma (known as baryon acoustic oscillations, or BAO), which leave an imprint on the CMB power spectrum.
• These imprints can be used to constrain the abundance and density fluctuations of dark matter, with CMB data providing strong limits on the cold dark matter (CDM) model. Anomalies in the CMB—such as deviations from the expected lensing of the CMB or small-scale power—could indicate the presence of exotic dark matter candidates.

2. Baryon Acoustic Oscillations (BAO) and Structure Formation

• BAO refer to periodic fluctuations in the density of visible matter (baryons) caused by sound waves traveling through the primordial plasma before recombination. These oscillations serve as a “standard ruler” that helps measure the expansion rate of the universe.
• The pattern of BAO, when combined with CMB data, provides a direct measurement of the matter density parameter (Ω_m) and the dark matter density (Ω_dm). Anomalies in the BAO measurement, especially at small scales, could suggest interactions or properties of dark matter that differ from those predicted by standard CDM.
• For exotic candidates like dark photons or ultra-light scalar fields, the sound waves in the early universe would behave differently due to the additional interactions or light mass of these particles. This could modify the sound speed in the early universe and alter the observed BAO patterns, constraining the viability of these candidates.

3. Weak Lensing Surveys and Structure Growth

• Weak gravitational lensing occurs when the gravitational field of large-scale structures (such as galaxy clusters) distorts the path of background light, allowing us to map the distribution of matter in the universe (including dark matter).
• The weak lensing surveys allow for precise measurements of galaxy shapes and the distribution of matter on cosmological scales. These surveys help determine how dark matter interacts with regular matter and how it clusters in large structures.
• Deviations in the lensing measurements can highlight differences in the clustering properties of dark matter or indicate the presence of additional forms of dark matter like dark photons, ultra-light scalar fields, or primordial black holes.
  • Dark photons could interact with standard matter via a new electromagnetic force, potentially altering the clustering of dark matter and its contribution to structure growth.
  • Ultra-light scalar fields could lead to fuzzy dark matter scenarios, where the dark matter behaves more like a fluid, suppressing small-scale structure formation and altering the growth of cosmic structures.
  • Primordial black holes (PBHs) could contribute to dark matter in a compact, non-interacting form and affect the growth of structure differently than CDM, leading to unique signatures in weak lensing maps.

4. Exotic Dark Matter Candidates

• Dark Photons:
  • Dark photons are hypothesized to be the gauge bosons of a new force that interacts with both dark matter and standard model particles. The kinetic mixing between dark photons and regular photons could potentially leave distinct signatures in CMB and BAO data, especially in the early universe. Such interactions could lead to deviations in the sound waves and matter distribution compared to CDM, offering clues about the presence of dark photons.
• Ultra-light Scalar Fields (Axions):
  • Ultra-light scalar fields, such as axions, are another potential dark matter candidate. These fields would have very small masses, which means they would not cluster as tightly as CDM. In the early universe, this could lead to fuzzy dark matter that behaves as a coherent wave rather than individual particles. This would suppress small-scale structure formation and alter the distribution of matter, as observed in both the CMB and BAO.
  • CMB anisotropies could be sensitive to the effects of these ultra-light scalar fields on the early universe’s thermal history. The lack of small-scale power seen in current surveys could be interpreted as a sign of such a component of dark matter.
• Primordial Black Holes (PBHs):
  • Primordial black holes could also be a component of dark matter. These black holes, formed in the early universe, would not interact via conventional forces and could act as dark matter candidates that do not participate in the normal formation of structures. If PBHs are abundant, they could leave distinctive signatures in weak lensing surveys, which map the matter distribution.
  • PBHs might also provide exotic features in the early universe dynamics, potentially influencing inflation and the formation of early structures in unique ways.

5. Dark Matter and Cosmic Inflation

• Cosmic inflation refers to the period of exponential expansion in the very early universe, driven by a hypothetical scalar field. The properties of dark matter could be connected to inflationary dynamics in the sense that certain types of dark matter candidates—especially light dark matter such as axions—could be produced during inflation.
• Inflationary models predict that the early universe was in a highly energetic state, and the interactions between dark matter particles and the inflaton (the field responsible for inflation) could leave imprints on the cosmic structure. For example, the energy density of dark matter at the end of inflation would set the stage for the formation of galaxies, clusters, and larger-scale structures.
• If dark matter is composed of exotic candidates like dark photons or ultra-light scalar fields, their properties could alter the inflationary dynamics, impacting both reheating and the formation of the cosmic structure.

The latest CMB anisotropies, BAO measurements, and weak lensing surveys provide critical constraints on the properties and interactions of dark matter. These observations help refine our understanding of how dark matter behaves in the early universe and its role in structure formation. Exotic dark matter candidates like dark photons, ultra-light scalar fields, and primordial black holes could offer alternative explanations for the small-scale anomalies observed in the cosmic structure. The interplay between dark matter and cosmic inflation provides an exciting avenue for future research, as the exact nature of dark matter continues to evolve beyond the standard CDM model.