Curvature profiles as initial conditions for primordial black hole formation

TL;DR

This paper develops an analytical and numerical framework to study primordial black hole formation during the early universe by relating initial curvature profiles to density and velocity perturbations, considering various cosmological fluids.

Contribution

It introduces a method to specify initial conditions via curvature profiles and derives analytic solutions for density and velocity, enabling comprehensive PBH formation analysis.

Findings

Analytic solutions for density and velocity as pure growing modes.

Numerical evolution of different initial curvature configurations.

Framework applicable to various cosmological fluid mixtures.

Abstract

This work is part of an ongoing research programme to study possible Primordial Black Hole (PBH) formation during the radiation dominated era of the early universe. Working within spherical symmetry, we specify an initial configuration in terms of a curvature profile, which represents initial conditions for the large amplitude metric perturbations, away from the homogeneous Friedmann Robertson Walker model, which are required for PBH formation. Using an asymptotic quasi-homogeneous solution, we relate the curvature profile with the density and velocity fields, which at an early enough time, when the length scale of the configuration is much larger than the cosmological horizon, can be treated as small perturbations of the background values. We present general analytic solutions for the density and velocity profiles. These solutions enable us to consider in a self-consistent way the formation of PBHs in a wide variety of cosmological situations with the cosmological fluid being treated as an arbitrary mixture of different components with different equations of state. We show that the analytical solutions for the density and velocity profiles as functions of the initial time are pure growing modes. We then use two different parametrisation for the curvature profile and follow numerically the evolution of a range of initial configuration.