The dark matter “core-cusp” problem refers to the discrepancy between predictions made by Cold Dark Matter (CDM) simulations and the actual observed distribution of dark matter in the centers of galaxy halos, especially in the Local Group. In CDM models, simulations predict that dark matter should form cusps (sharply increasing density) in the inner regions of galaxy halos, particularly in smaller galaxies. However, observations suggest that many small galaxies exhibit cores (flattened density profiles) instead of the predicted cusps. This discrepancy creates tension between CDM-based simulations and the observed distribution of galactic halos, especially at smaller scales, and challenges the adequacy of CDM in explaining the detailed structure of galaxies.

Impact on Cold Dark Matter (CDM) Simulations

• Predicted Cusp Profiles: In the CDM paradigm, the gravitational collapse of dark matter during the formation of halos leads to a steep increase in density toward the center, resulting in a cusp in the central regions of smaller galaxies.
• Observed Cores: However, many dwarf galaxies and satellite galaxies in the Local Group show evidence of core-like profiles (a smooth, flattened density near the center). These observations suggest that the actual density is much lower than predicted by CDM simulations, particularly in the central regions of these small galaxies.

The core-cusp problem highlights that the CDM model may not fully account for the observed galactic structures, especially at small scales. This discrepancy undermines the confidence in CDM as the sole explanation for galaxy formation and dark matter behavior.

Implications for Alternative Dark Matter Models

1. Self-Interacting Dark Matter (SIDM):
   • SIDM Theory: SIDM posits that dark matter particles interact with each other via self-interactions, unlike the weakly interacting particles assumed in CDM.
   • Effects on Structure Formation: The self-interactions in SIDM lead to more isotropic dark matter distributions, which help smooth out the cusps predicted by CDM. These interactions can transfer energy within the halo, causing the dark matter to redistribute and form cores rather than steep cusps in the central regions of galaxies.
   • Relevance to Core-Cusp Problem: SIDM could resolve the core-cusp problem by generating more core-like profiles in small galaxies. This has been suggested as a potential solution to the tension between CDM predictions and observed galaxy structures.
2. Fuzzy Dark Matter (FDM):
   • FDM Theory: Fuzzy dark matter consists of ultralight bosons, which behave more like waves rather than particles, leading to quantum effects that modify the behavior of dark matter at small scales.
   • Effects on Structure Formation: In FDM models, the wave-like nature of dark matter suppresses the formation of small-scale structure. At the center of galaxies, the quantum pressure of these bosons prevents the formation of steep density cusps, leading to core-like profiles.
   • Relevance to Core-Cusp Problem: The fuzzy nature of FDM helps in producing core-like profiles at small scales and could provide a natural explanation for the observed distribution of dark matter in dwarf galaxies and satellite galaxies in the Local Group, alleviating the core-cusp problem.

Contributions to the Growing Tension

• The core-cusp problem intensifies the tension between observations and CDM simulations at small scales. CDM predicts a much steeper dark matter density profile in the centers of galaxies, but observations show that many smaller galaxies (such as those in the Local Group) have much flatter, core-like profiles.
• The core-cusp problem adds weight to the argument that CDM alone may not be sufficient to explain small-scale structure formation, especially in the context of satellite galaxies and dwarf galaxies.

Implications for Structure Formation at Small Scales

• CDM: Predicts smaller, denser halos with cusps in the center, which might be inconsistent with the observed distribution of galaxies at small scales. These inconsistencies are particularly evident in satellite galaxies and ultra-faint dwarf galaxies, where the predicted number and distribution of satellite galaxies are often higher than observed.
• SIDM: By introducing self-interactions, SIDM provides a way to smooth out these cusps and create more realistic core profiles, improving the agreement between simulations and observations at small scales.
• FDM: The quantum nature of FDM suppresses small-scale power and leads to smoother, core-like profiles, offering an alternative to the steep cusps predicted by CDM and aligning better with observations at small scales.

The core-cusp problem significantly contributes to the growing tension between CDM simulations and observed galaxy structures, especially at small scales. It challenges the CDM model’s predictions of dark matter density profiles in smaller galaxies. Alternative models such as Self-Interacting Dark Matter (SIDM) and Fuzzy Dark Matter (FDM) offer potential solutions by producing core-like profiles, which align better with the observed distribution of satellite and dwarf galaxies. These models suggest that dark matter’s properties might differ from the assumptions of CDM, especially at smaller scales, providing an avenue for resolving current discrepancies in galaxy formation theories.

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.