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.

Your question touches on several cutting-edge topics in theoretical physics, including the interplay between dark matter, gravity, and quantum theories at the Planck scale, as well as the application of holographic principles and quantum information theory. Here’s a structured exploration of these ideas:

1. Quantum Gravitational Effects and Dark Matter at the Planck Scale

• At the Planck scale ($10^{-35}10^\{-35\}$meters), quantum gravitational effects are expected to dominate, and the classical description of spacetime breaks down. In this regime, theories like quantum field theory (QFT) in curved spacetime and quantum gravity frameworks (e.g., string theory or loop quantum gravity) are necessary.
• Dark matter, though currently described effectively as interacting gravitationally and weakly (if at all) with other particles, may have quantum origins linked to early universe dynamics. For instance, during the inflationary period or a quantum gravity-dominated phase, interactions between dark matter particles and the quantum gravitational field could seed the primordial density perturbations that later grew into cosmic structures.

2. Formation of Cosmic Structures

• Gravity, as the dominant large-scale force, governs the clumping of dark matter into halos and the eventual formation of galaxies and other cosmic structures. Quantum gravitational effects might influence the initial conditions for these structures through mechanisms like quantum fluctuations during inflation.
• Understanding whether dark matter has a purely particle-based nature (e.g., WIMPs or axions) or arises from a more exotic quantum field framework (such as a Bose-Einstein condensate of ultralight particles) is critical to refining models of structure formation.

3. Quantum Field Theory and String Theory

• Quantum Field Theory: QFT provides the foundation for exploring the interactions of dark matter with the Standard Model, though direct evidence for such interactions remains elusive. Non-perturbative QFT approaches, such as lattice simulations, could probe hypothetical self-interactions of dark matter particles.
• String Theory: In string theory, dark matter candidates like the axion emerge naturally as moduli or other light scalar fields. String theory also provides a framework for incorporating quantum gravity into a unified description of all forces, which could clarify dark matter’s fundamental properties and interactions.

4. Insights from Black Hole Entropy and Holography

• The Bekenstein-Hawking entropy of black holes, proportional to the area of the event horizon, suggests a deep connection between gravity, quantum mechanics, and information theory. Extending this principle, the holographic principle posits that the information content of a volume of space can be encoded on its boundary.
• AdS/CFT Correspondence: This duality, central to string theory, relates gravitational theories in an Anti-de Sitter (AdS) space to conformal field theories (CFT) on its boundary. Insights from AdS/CFT might reveal how dark matter could be a manifestation of deeper quantum information principles, particularly if dark matter is tied to holographically dual descriptions.
• Some theories speculate that dark matter might not be a fundamental particle but rather a macroscopic manifestation of quantum informational structures, akin to emergent phenomena seen in condensed matter physics.

5. Dark Matter as a Quantum Information Phenomenon

• Theories linking dark matter to quantum information suggest that it might represent a form of entropy or quantum state encoded in the universe’s large-scale structure. If so, the study of dark matter could benefit from tools developed in quantum information theory, such as entanglement entropy and tensor network approaches.

6. Future Directions

• Experimental Probes: Observations of gravitational waves, black hole mergers, and the cosmic microwave background (CMB) might reveal signatures of quantum gravitational effects and their influence on dark matter.
• Theoretical Developments: Advances in non-perturbative quantum gravity, numerical simulations of holographic models, and novel insights into string theory could further illuminate dark matter’s origins and its role in cosmic evolution.

By synthesizing these interdisciplinary approaches, a more unified understanding of dark matter, gravity, and the quantum fabric of the universe may emerge