http://arxiv.org/abs/2206.01150
The phenomenology of primordial black holes (PBHs) physics, and the associated PBH abundance constraints, can be used in order to probe the early-universe evolution. In this work, we focus on the bounce realization within $F(R)$ modified gravity and we investigate the corresponding PBH behavior. In particular, we calculate the energy density power spectrum at horizon crossing time as a function of the involved theoretical parameters, and then we extract the PBH abundance in the context of peak theory, considering the non-linear relation between the density contrast and the comoving curvature perturbation, as well as the critical collapse law for the PBH masses. We first calculate the PBH mass function, and then we extract the PBH abundance $\Omega_\mathrm{PBH,f}$ at formation time as a function of the model parameters, namely the involved $F(R)$ parameter $\alpha$ and the Hubble parameter at the transition time from the bounce to the radiation dominated epoch $H_\mathrm{RD}$. Interestingly, we find that in order to have a significant black hole production, namely $10^{-10}<\Omega_\mathrm{PBH,f}<1$, $H_\mathrm{RD}$ and $\alpha$ should lie roughly within the ranges $10^{-7}M_\mathrm{Pl}\leq H_\mathrm{RD}\leq 10^{-6}M_\mathrm{Pl}$, $10^{-9}M_\mathrm{Pl}\leq H_\mathrm{RD}\leq 2\times 10^{-9}M_\mathrm{Pl}$ and $10^{-30}M^2_\mathrm{Pl}\leq \alpha \leq 10^{-12}M^2_\mathrm{Pl}$ respectively. Finally, we show that the excluded region corresponding to PBH overproduction forms a closed ring.
S. Banerjee, T. Papanikolaou and E. Saridakis
Fri, 3 Jun 22
20/57
Comments: 20 pages without appendices (27 in total), 6 figures
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