Black hole formation in a contracting universe

TL;DR

This paper investigates the conditions under which density perturbations in a contracting universe grow sufficiently to form black holes, analyzing different initial conditions and fluid types to understand their implications for early universe models.

Contribution

It provides a comprehensive analysis of black hole formation in contracting universes, considering various initial conditions and fluid equations of state, with implications for matter bounce cosmology.

Findings

Large inhomogeneities can form black holes before Planck scale in dust-like fluids.

No black holes form before Planck scale in radiation-dominated fluids.

Black hole formation is sensitive to the initial fluctuation conditions and fluid properties.

Abstract

We study the evolution of cosmological perturbations in a contracting universe. We aim to determine under which conditions density perturbations grow to form large inhomogeneities and collapse into black holes. Our method consists in solving the cosmological perturbation equations in complete generality for a hydrodynamical fluid. We then describe the evolution of the fluctuations over the different length scales of interest and as a function of the equation of state for the fluid, and we explore two different types of initial conditions: quantum vacuum and thermal fluctuations. We also derive a general requirement for black hole collapse on sub-Hubble scales, and we use the Press-Schechter formalism to describe the black hole formation probability. For a fluid with a small sound speed (e.g., dust), we find that both quantum and thermal initial fluctuations grow in a contracting universe, and the largest inhomogeneities that first collapse into black holes are of Hubble size and the collapse occurs well before reaching the Planck scale. For a radiation-dominated fluid, we find that no black hole can form before reaching the Planck scale. In the context of matter bounce cosmology, it thus appears that only models in which a radiation-dominated era begins early in the cosmological evolution are robust against the formation of black holes. Yet, the formation of black holes might be an interesting feature for other models. We comment on a number of possible alternative early universe scenarios that could take advantage of this feature.