[Paper Review] An Holographic Cosmology

T. Banks, Willy Fischler|ArXiv.org|Nov 15, 2001

Dark Matter and Cosmic PhenomenaPhysics and Astronomy9 references57 citations

TL;DR

This paper proposes a holographic cosmology in which the early universe is dominated by a dense gas of black holes with equation of state $p = \rho$, satisfying the holographic entropy bound. Quantum fluctuations in this state generate a scale-invariant spectrum of density perturbations, leading to a radiation-dominated phase after Hawking decay; however, causality constraints limit the observable scale of these fluctuations to $10^7$ times smaller than the horizon, suggesting limitations in the field-theoretic treatment of the $p=\rho$ regime.

ABSTRACT

We present a new cosmological model, based on the holographic principle, which shares many of the virtues of inflation. The very earliest semiclassical era of the universe is dominated by a dense gas of black holes, with equation of state $p=ρ$. Fluctuations lead to an instability to a phase with a dilute gas of black holes, which later decays via Hawking radiation to a radiation dominated universe. The quantum fluctuations of the initial state give rise to a scale invariant spectrum of density perturbations, for a range of scales. We point out a problem, that appears to prevent the range of scales predicted by the model from coinciding with the range where such a spectrum has been observed. We speculate that this may be related to our field theoretic treatment of fluctuations in the highly holographic $p=ρ$ background. The monopole problem is solved in a manner completely different from inflationary models, and a relic density of highly charged extremal black monopoles is predicted. We discuss the nature of the entropy and flatness problems in our model.

Motivation & Objective

• To develop a non-inflationary cosmological model based on the holographic principle that resolves the horizon and flatness problems.
• To explain the origin of primordial density perturbations via quantum fluctuations in a $p=\rho$ black hole fluid.
• To address the monopole problem through the formation of highly charged extremal black monopoles instead of conventional GUT monopoles.
• To reconcile the reheat temperature, nucleosynthesis constraints, and dark matter in a holographic framework.
• To explore the implications of CP violation and baryogenesis from dyonic black hole decay in a $\theta$-angle coupled system.

Proposed method

• Model the early universe as a homogeneous, dense gas of black holes with $p = \rho$, saturating the Fischler-Susskind-Bousso entropy bound.
• Use quantum and statistical fluctuations in the $p=\rho$ state to trigger a phase transition to a dilute gas of black holes with $p=0$, which later decay via Hawking radiation.
• Apply standard quantum field theory in curved spacetime to compute long-range two-point correlations of the gravitational field in the $p=\rho$ background.
• Derive the scale-invariant nature of density fluctuations by showing that their amplitude at the horizon scale is independent of horizon size.
• Construct a scenario where black holes in the $p=\rho$ phase merge, increasing their charge, and eventually form highly charged extremal black monopoles.
• Use constraints from nucleosynthesis and monopole relic density to fix the parameter $P_0$, the probability of forming large dilute gas regions.

Experimental results

Research questions

• RQ1 Can a $p=\rho$ black hole fluid provide a viable alternative to inflation for solving the horizon and flatness problems?
• RQ2 How do quantum fluctuations in the $p=\rho$ state lead to a scale-invariant spectrum of density perturbations?
• RQ3 Why does the predicted scale of fluctuations fall short of the observed CMB scale by a factor of $10^7$, and what does this imply about the validity of the field-theoretic treatment?
• RQ4 Can the monopole problem be solved via the formation of highly charged extremal black monopoles instead of conventional GUT monopoles?
• RQ5 What are the implications of CP- and baryon-number-violating Hawking decay from dyonic black holes for baryogenesis and the matter-antimatter asymmetry?

Key findings

• The $p=\rho$ black hole fluid provides a non-inflationary solution to the horizon and flatness problems by saturating the holographic entropy bound.
• Quantum fluctuations in the $p=\rho$ state generate a scale-invariant spectrum of density perturbations, which persists after conversion to classical inhomogeneities.
• The model predicts a reheat temperature below the nucleosynthesis scale, consistent with cosmological constraints.
• The relic density of highly charged extremal black monopoles is safely below observational limits but may be detectable in galactic centers.
• The scale of the predicted fluctuation spectrum is limited to $10^7$ times smaller than the current horizon radius, indicating a potential breakdown of the field-theoretic treatment in the highly holographic $p=\rho$ regime.
• The model suggests that CP- and baryon-number-violating decay of charged black holes may naturally generate the observed baryon asymmetry.