Constraining $F(R)$ bouncing cosmologies with primordial black holes

TL;DR

This paper explores how an early F(R) gravity bouncing phase influences primordial black hole formation, providing constraints on model parameters to avoid overproduction of gravitational waves before Big Bang Nucleosynthesis.

Contribution

It introduces a novel F(R) gravity bouncing model to study PBH formation during radiation era and derives constraints on model parameters from observational limits.

Findings

Constraint on parameter α: α ≤ 10^{-19} M_{Pl}^2

Upper limit on Hubble rate at reheating: H_{RD} < 10^{-10} M_{Pl}

Avoids GW overproduction from early PBH era

Abstract

The phenomenology of primordial black hole (PBH) physics and the associated PBH abundance constraints, can be used in order to probe the physics of the early Universe. In this work, we investigate the PBH formation during the standard radiation-dominated era by studying the effect of an early F(R) modified gravity phase with a bouncing behavior which is introduced to avoid the initial spacetime singularity problem. In particular, we calculate the energy density power spectrum at horizon crossing time and then we extract the PBH abundance in the context of peak theory as a function of the parameter $\alpha$ of our $F(R)$ gravity bouncing model at hand. Interestingly, we find that in order to avoid GW overproduction from an early PBH dominated era before Big Bang Nucleosynthesis (BBN), $\alpha$ should lie within the range $\alpha\leq 10^{-19}M^2_\mathrm{Pl}$. This constraint can be translated to a constraint on the energy scale at the onset of the Hot Big Bang (HBB) phase, $H_\mathrm{RD}\sim \sqrt{\alpha}/2$ which can be recast as $H_\mathrm{RD}< 10^{-10}M_\mathrm{Pl}$.