Can Primordial Black Holes Be Seeds for Early Galaxies in Models Satisfying the Covariant Entropy Bound?

Technical Summary: Primordial Black Holes as Seeds for Early Galaxies in Models Satisfying the Covariant Entropy Bound

Problem Statement
The authors address the tension between cosmological models satisfying the Covariant Entropy Bound (CEB) and observational data regarding early galaxy formation and dark matter. Previous iterations of the authors' Holographic Space-Time (HST) model successfully fit Cosmic Microwave Background (CMB) data by postulating that the early universe consisted of horizon volumes containing tiny black holes that decayed into radiation, triggering the Hot Big Bang. However, this specific configuration failed to account for the massive seeds required to form the early supermassive black holes observed by the James Webb Space Telescope (JWST). Furthermore, standard field-theoretic inflation models are argued to violate the CEB by requiring an excessive number of independent quantum degrees of freedom within a small causal diamond, leading to Trans-Planckian problems. The central problem is to construct a cosmological initial condition that satisfies the CEB, reproduces CMB observations, accounts for dark matter, and provides sufficient massive seeds for early galaxies without violating fundamental quantum gravitational principles.

Methodology
The paper employs a dual approach combining semi-classical General Relativity (GR) solutions with a speculative quantum gravity framework based on Holographic Space-Time (HST) and Matrix Models.

1. Theoretical Framework (HST and CEB): The authors utilize the principle that the CEB implies a flat Friedmann-Robertson-Walker (FRW) universe with an equation of state $p = \pm \rho$. In this framework, the "empty diamond state" (maximal entropy) corresponds to a featureless vacuum. Localized excitations (like black holes) represent low-entropy states. The authors argue that the most probable state for a constrained system is a single huge black hole, but anthropic or observational constraints require a compromise: a distribution of black holes that avoids "cosmic disasters" (domination by a few huge holes) while allowing for structure formation.
2. Initial Conditions via Israel Junctions: To resolve the JWST seed problem, the authors modify the initial conditions. Instead of uniform tiny black holes, they postulate a random distribution of larger Primordial Black Holes (PBHs). These larger PBHs are modeled as "ashes of the heat death" of small, maximal entropy universes (asymptotically de Sitter spaces with radius $R_n$). These de Sitter patches are glued into the interior of slightly larger black holes within the expanding FRW universe using Israel junction conditions. This process is interpreted via the ER=EPR paradigm, where the collapse of the de Sitter horizon represents thermalization with the larger black hole, and the Einstein-Rosen bridge represents the entanglement between the subsystem and the larger system.
3. Matrix Model Formulation: The authors describe the universe using a matrix model of finite-dimensional Hilbert bundles over time-like geodesics. The degrees of freedom are represented by matrix-valued Dirac fields. The initial state is a block-diagonal matrix where each block corresponds to a specific horizon volume (either a small $R_I$ or a large $R_n$). The evolution involves the gradual "turning on" of off-diagonal elements as blocks come into causal contact, simulating the merging of black holes and the emergence of homogeneity and isotropy.
4. Structure Formation Analysis: In Appendix A, the authors perform a Press-Schechter analysis and numerical simulations to test if small black holes can merge to form solar-mass seeds by the end of radiation domination. They conclude that standard clustering of small black holes is insufficient. Instead, they find that the initial distribution must include black holes significantly larger than the horizon size at the end of slow-roll inflation, which are already present as "unconstrained horizon volumes" in the matrix model.

Key Contributions and Results

• Reinterpretation of PBHs: The paper proposes that large PBHs are the remnants of small, maximal entropy universes that have undergone "heat death" and thermalized with the bulk universe. This provides a geometric realization of the "birth of a baby universe inside a black hole" Penrose diagram, reinterpreted through the lens of ER=EPR.
• Resolution of CMB and JWST Tensions: The model successfully fits CMB data by retaining the slow-roll inflation mechanism within small horizon volumes (generating the necessary density fluctuations) while introducing a random distribution of larger PBHs. These larger PBHs serve as the seeds for the early galaxies and supermassive black holes observed by JWST.
• Dark Matter Mechanism: The model offers a unified explanation for dark matter. It posits that dark matter consists of:
  1. Stable Planck-scale remnants from the decay of the dominant population of small PBHs (replacing the previous $Z_N$ gauge charge stabilization requirement).
  2. A fraction of the cosmologically stable, heavier PBHs from the random distribution.
     The mass spectrum is peaked in the currently allowed window ($2 \times 10^{22} - 10^{28} L_P$) with a tail extending to solar masses and above, with a weight of $10^{-3} - 10^{-5}$.
• Matrix Model Dynamics: The authors demonstrate how homogeneity and isotropy emerge from a fundamentally random initial state in the matrix model. The angular distribution of black holes is encoded in the consistency conditions (entanglement spectra) between different geodesics rather than in the diagonal elements of a single matrix.
• Failure of Small-to-Large Merging: The analysis in Appendix A explicitly shows that relying solely on the merging of small, horizon-sized black holes cannot produce the necessary solar-mass seeds by the end of radiation domination. This necessitates the postulation of pre-existing large PBHs in the initial conditions.

Significance and Claims
The authors claim that their model represents a "generalization" of previous HST models that resolves the conflict between CEB-satisfying cosmologies and early galaxy observations. The significance lies in:

1. Eliminating Trans-Planckian Problems: By satisfying the CEB, the model avoids the need for quantum field theory to hold at distances far below the Planck length, a common issue in standard inflationary models.
2. Naturalness of Initial Conditions: The model argues that the most mathematically probable initial conditions (saturating the CEB) lead to a universe dominated by a single huge black hole or no localized objects. The observed universe is a result of a "compromise" initial condition that balances entropy maximization with the requirement for localized excitations (galaxies).
3. Economical Dark Matter: The model suggests that dark matter does not require new particle physics beyond the Standard Model (other than the existence of PBHs and their remnants), as the spectrum of PBHs naturally accounts for the observed dark matter density and the early galaxy seeds.
4. Conceptual Shift: The paper reframes the origin of the universe's structure not as an inflationary expansion of quantum fluctuations, but as the thermalization and decay of a collection of independent, maximal entropy subsystems (small universes) that merge into a single causal structure.

The authors remain modest regarding the specific "biothropic" or anthropic selection of the black hole mass spectrum, acknowledging that the current work focuses on finding a spectrum that fits the maximum amount of data rather than deriving it from a complete theory of life or a multiverse weight distribution. They note that further theoretical and observational work is required to fully explore the hypothesis that a small fraction of black holes above the solar mass scale at the beginning of matter domination is the key to early galaxy formation.