MG11 
Talk detail
 

 Participant 

Institution

Session

Talk

Abstract

Curvature profiles as initial conditions for primordial black hole formation

This work is part of an ongoing research programme to study possible Primordial Black Hole (PBH) formation in the early universe. Working within spherical symmetry, we specify an initial configuration in terms of a curvature profile $K(r)$, which represents initial conditions for the large amplitude metric perturbations, away from the homogeneous Friedmann Robertson Walker model, which are required for PBH formation. This curvature profile $K(r)$ is directly linked to the time- independent co-moving curvature perturbation $\mathcal{R}$. Using an asymptotic quasi-homogeneous solution, we relate $K(r)$ 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 given 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 similar to those for pure growing modes in standard cosmological perturbation theory. We then use two different parametrisations for $K(r)$ to follow numerically the evolution of the initial configuration, restricting attention to the formation of PBHs in the radiation dominated era. The results obtained confirm the possibility of forming primordial black holes if the perturbation amplitude exceeds a certain threshold but cases examined so far have not shown any evidence for the presence of shock formation in supercritical collapse as was previously observed. We have introduced an adaptive gridding algorithm in order to investigate more closely the issue of whether there is a minimum black-hole mass in critical collapse when initial conditions of the growing-mode type are used. This investigation is currently ongoing.