The “large-scale structure” (LSS) of the universe refers to the distribution of galaxies, clusters, superclusters, and voids across the cosmos. These structures provide critical insights into the nature of dark matter (DM), as it is thought to play a fundamental role in the formation and evolution of these structures. The presence of dark matter (including various models like cold dark matter (CDM) and self-interacting dark matter (SIDM)) has significant implications for LSS, and discrepancies between the predictions of cosmological simulations and actual observations have raised important questions about the properties of dark matter. Below, I explore how the LSS challenges our understanding of dark matter properties, particularly in the context of SIDM, and how future surveys like the EUCLID mission can help resolve these tensions.

Large-Scale Structure and Dark Matter

• The LSS of the universe includes the formation of galaxy clusters, superclusters, and voids, which are large regions of space with relatively few galaxies. The formation of these structures is governed by the interplay between gravity and the distribution of dark matter. Dark matter is believed to have provided the gravitational scaffolding for the formation of galaxies and clusters, which then evolved into the structures we observe today.

Challenges for Our Understanding of Dark Matter Properties

1. Cold Dark Matter (CDM) and the “Core-Cusp” Problem

• Cold dark matter (CDM) is the leading candidate for dark matter, assuming it interacts weakly with ordinary matter and itself. CDM predicts the formation of cuspy halos—dense, concentrated regions of dark matter at the center of galaxies and clusters.
• However, observations of galactic halos show a core (i.e., a more spread-out, less concentrated distribution of dark matter) rather than the predicted cusp. This discrepancy is known as the core-cusp problem.
• The formation of large-scale structures like superclusters and voids is influenced by the behavior of dark matter at smaller scales. The core-cusp problem raises the possibility that dark matter behaves differently than predicted by standard CDM, particularly in smaller systems like dwarf galaxies.

2. Self-Interacting Dark Matter (SIDM)

• Self-interacting dark matter (SIDM) proposes that dark matter particles interact with each other via a new force, in addition to gravity. These interactions would cause dark matter to redistribute within galaxies and clusters, smoothing out the central density profiles and potentially resolving the core-cusp problem.
• SIDM models predict that dark matter halos should have a less cuspy and more uniform distribution in the centers of galaxies and that they could affect the dynamics of galaxy formation and clustering. This would also influence the observed LSS, particularly in terms of the clustering of galaxies and the distribution of voids.

3. Tension Between Simulations and Observations

• Cosmological simulations based on CDM predict that dark matter should form very dense halos around galaxies, leading to structures like galaxy clusters with a high concentration of dark matter at the center.
• Observations of galaxy clusters and other large-scale structures, however, do not always match these predictions, particularly at smaller scales. This tension points to the possibility that dark matter interactions (such as those in SIDM) might be altering the way galaxies and clusters form, leading to a less concentrated distribution of dark matter and a smoothing of smaller-scale structures.

Role of Future Surveys, Like EUCLID

The EUCLID mission, set to launch in the near future, will be one of the most important tools for resolving tensions between cosmological simulations and observations of large-scale structure. Here’s how it will help:

1. Measuring the Distribution of Galaxies and Clusters

• EUCLID is designed to measure the distribution of galaxies and galaxy clusters across large areas of the sky with great precision. By accurately mapping out the 3D distribution of galaxies and clusters, EUCLID will provide data that can be compared to simulations of structure formation under different dark matter models.
• By comparing the observed distribution of galaxies and clusters to predictions made by simulations using SIDM and CDM, EUCLID will help identify which model most accurately explains the observed data. The mission will offer insights into how dark matter affects the growth of structures at large scales.

2. Constraining Dark Matter Properties

• EUCLID will also help constrain the properties of dark matter, including its interaction rate and mass, by providing detailed data on the growth of cosmic structures and how they evolve over time.
• The mission will focus on measuring the distortions in the cosmic structure due to the presence of dark energy and dark matter. By studying the shape of galaxy clusters and superclusters, voids, and the large-scale distribution of galaxies, EUCLID will help test whether dark matter behaves as predicted by CDM or whether SIDM models are needed to explain the observed discrepancies.

3. Mapping Cosmic Voids and the Impact of Dark Matter

• One of the key areas where SIDM may differ from CDM is in the formation and distribution of voids—large regions of space with very few galaxies.
• SIDM would lead to a different distribution of dark matter in the universe, which in turn would affect the number, size, and distribution of voids. EUCLID‘s precision in mapping these voids will help determine whether the void distribution matches predictions from simulations based on CDM or whether alternative models like SIDM can better explain the observed patterns.

4. Weak Lensing and Gravitational Effects

• EUCLID will measure weak gravitational lensing, where the gravitational influence of large structures (such as galaxy clusters) bends the light from more distant objects. This technique is sensitive to the distribution of dark matter because it measures how dark matter affects the curvature of space-time.
• This will allow EUCLID to provide direct measurements of the dark matter content in galaxy clusters and large-scale structures. The way that dark matter halos are distributed around galaxies and clusters will help constrain whether SIDM or CDM better explains the observed data.

The large-scale structure of the universe presents a critical challenge to our understanding of dark matter, particularly in terms of the formation of superclusters and voids. The tension between predictions from cold dark matter (CDM) simulations and actual observations of galactic clustering and the distribution of voids has led to the exploration of alternative models, such as self-interacting dark matter (SIDM).

Future surveys, particularly the EUCLID mission, will play a pivotal role in resolving these tensions. By providing detailed measurements of the distribution of galaxies, voids, and galaxy clusters, along with weak lensing data, EUCLID will offer new insights into the nature of dark matter, testing the predictions of both SIDM and CDM models. Ultimately, these findings will help to refine our understanding of the cosmological parameters that govern the growth of structures in the universe and lead to a better grasp of dark matter’s role in shaping the cosmos.

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.