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 question of whether axions can account for dark matter is a complex issue that intersects with several fields of study, including cosmology, particle physics, and astrophysics. Constraints on dark matter, particularly axions, come from various sources, including the cosmic microwave background (CMB) power spectrum, large-scale galaxy surveys, and direct detection experiments like XENON1T, as well as astrophysical observations. Let’s break down the evidence and challenges related to axions as a potential dark matter candidate.

Axions as a Dark Matter Candidate

• Axions are hypothetical particles predicted by the Peccei-Quinn theory to solve the strong CP problem in quantum chromodynamics (QCD). These particles are ultra-light, and if they have the right properties, they could contribute to dark matter. Their extremely low mass and weak interactions with other particles make them an intriguing candidate for cold dark matter (CDM).

CMB Power Spectrum Constraints

• The CMB provides crucial insights into the early universe, particularly the fluctuations in the density of matter and radiation, which can be used to infer properties of dark matter. Key features of the CMB, like the angular power spectrum, depend on the density of different components of the universe, including dark matter.
• Axions (if they exist) can significantly affect the CMB power spectrum. Specifically:
  1. Axions as Cold Dark Matter (CDM): If axions make up dark matter, they would impact the early universe’s expansion rate and the growth of cosmic structures. Their presence would modify the sound horizon (the size of the largest sound waves in the early universe), which in turn would affect the CMB peaks.
  2. Axion Dark Matter Density: CMB data, particularly from Planck and WMAP missions, have been used to place upper limits on the density of axion-like particles (ALPs) in the universe. Constraints on dark matter from CMB observations suggest that axions could contribute to dark matter, but their mass must be extremely small (on the order of $10^{-22}eV10^\{-22\}\; \backslash text\{eV\}$10−22eV) for consistency with the observed CMB power spectrum.

Large-Scale Galaxy Surveys

• Surveys of large-scale cosmic structures, such as the Baryon Acoustic Oscillation (BAO) measurements and the Lyman-alpha forest in quasar spectra, provide further constraints on the properties of dark matter.
  • Axions’ Influence on Structure Formation: The presence of axions as dark matter would have different effects on structure formation compared to other dark matter models. Specifically, axions (due to their small mass) would suppress structure formation at smaller scales compared to cold dark matter. This would leave a distinct signature in the distribution of galaxies, halos, and the clustering of large-scale structures.
  • Large-scale surveys, including data from SDSS and DES, have found no significant deviation from the predictions made by the standard CDM model. The lack of evidence for extra suppression of small-scale structure supports the idea that axions must have a very small mass to avoid disrupting the observed cosmic structures.

Direct Detection Experiments (XENON1T)

• Direct detection experiments, such as XENON1T, search for interactions between dark matter particles and the standard model of particles. These experiments are sensitive to weakly interacting massive particles (WIMPs), but also test other candidates, including axions.
  • Axion Detection via Axion-Photon Coupling: Axions can interact with photons through an axion-photon coupling, a feature that allows axions to potentially be detected through photon conversion in strong magnetic fields.
  • XENON1T Results: In 2020, XENON1T set stringent limits on interactions between dark matter and nucleons, primarily aimed at WIMPs. However, its sensitivity to axions is less direct, though it has placed upper bounds on the possible axion-photon coupling, which limits the detectability of axions via direct detection experiments.
  • The mass of the axion affects how it could be detected. Ultra-light axions might not interact sufficiently in direct detection experiments like XENON1T, and the limits on axion-photon coupling are critical in determining whether axions are detectable in this manner.

Astrophysical Observations

• Axion-Photon Coupling: Astrophysical observations, such as the behavior of light passing through magnetic fields in galaxies or the supernova 1987A, can provide constraints on the axion-photon coupling constant. If axions are too efficient at converting into photons, they could have observable effects on stellar evolution or the cosmic microwave background.
  • Supernova 1987A: This supernova provided strong constraints on the axion’s interaction with photons. If axions were abundant and could efficiently convert into photons, they would carry away energy from the supernova, altering the light curve. The non-observation of such effects puts upper bounds on the axion-photon coupling.
  • Cosmic Magnetic Fields: Axion-photon interactions could also produce observable effects in galactic and intergalactic magnetic fields, but current astrophysical data have not shown any such evidence, further tightening the constraints on axion properties.

Challenges in Reconciling Findings

1. Mass Range and Detection: The mass of axions that would fit cosmological constraints from the CMB and large-scale surveys is extremely small (around $10^{-22}eV10^\{-22\}\; \backslash text\{eV\}$10−22eV). However, this small mass makes them very difficult to detect in direct detection experiments like XENON1T, which are designed for much heavier dark matter candidates like WIMPs.
2. Axion-Photon Coupling: The limits on the axion-photon coupling derived from astrophysical observations and direct detection experiments often conflict with the range needed for axions to be a significant dark matter component. If the axion-photon coupling is too strong, it would contradict astrophysical constraints, while if it’s too weak, axions may not be detectable by existing experiments.
3. Small-Scale Structure Suppression: While axions’ impact on large-scale structure formation is consistent with observations, their ability to suppress structure formation at smaller scales (such as in dwarf galaxies) has yet to be conclusively validated. This could be a challenge if axions are too light, as they might leave fewer structures or fail to form halos in ways that align with observations.

The constraints from the CMB, large-scale galaxy surveys, direct detection experiments, and astrophysical observations suggest that axions could contribute to dark matter, but their ultra-light mass poses challenges for direct detection and for reconciling all these findings. While their small mass allows them to fit with cosmological data and structure formation at large scales, their axion-photon coupling must be very weak to avoid conflicts with astrophysical limits. As a result, axions remain a viable but challenging candidate for dark matter, and more precise experiments and observations will be needed to further refine their properties and determine their role in the dark matter puzzle.