Enhance Primordial Black Hole Abundance through the Non-linear Processes around Bounce Point

TL;DR

This paper investigates how non-linear processes during a non-singular bounce in cosmology can significantly enhance primordial black hole abundance, using numerical solutions and modified probabilistic models.

Contribution

It introduces a detailed numerical analysis of non-linear density fluctuations during a bounce, demonstrating their role in increasing PBH formation beyond linear estimates.

Findings

Bounce phase can substantially increase PBH abundance.

Non-linear effects lead to non-Gaussian density fluctuation distributions.

Constraints on bounce parameters are derived from PBH abundance considerations.

Abstract

The non-singular bouncing cosmology is an alternative paradigm to inflation, wherein the background energy density vanishes at the bounce point, in the context of Einstein gravity. Therefore, the non-linear effects in the evolution of density fluctuations ($\delta \rho$) may be strong in the bounce phase, which potentially provides a mechanism to enhance the abundance of primordial black holes (PBHs). This article presents a comprehensive illustration for PBH enhancement due to the bounce phase. To calculate the non-linear evolution of $\delta \rho$, the Raychaudhuri equation is numerically solved here. Since the non-linear processes may lead to a non-Gaussian probability distribution function for $\delta \rho$ after the bounce point, the PBH abundance is calculated in a modified Press-Schechter formalism. In this case, the criterion of PBH formation is complicated, due to complicated non-linear evolutionary behavior of $\delta \rho$ during the bounce phase. Our results indicate that the bounce phase indeed has potential to enhance the PBH abundance sufficiently. Furthermore, the PBH abundance is applied to constrain the parameters of bounce phase, providing a complementary to the surveys of cosmic microwave background and large scale structure.