Primordial Black Hole Merger Rate in $f(R)$ Gravity

TL;DR

This paper calculates the primordial black hole merger rate within $f(R)$ gravity, revealing an enhancement over general relativity and potential observational signatures, aligning with gravitational wave data for certain PBH abundance.

Contribution

It introduces a novel calculation of PBH merger rates in $f(R)$ gravity, highlighting the effects of modified gravity on black hole formation and merger predictions.

Findings

Enhanced PBH merger rate in $f(R)$ gravity compared to GR.

Modulating $f_{R0}$ shifts the merger rate, offering observational signatures.

Merger rates are consistent with LIGO-Virgo-KAGRA data for $f_{PBH} extgreater{}0.1$.

Abstract

Primordial black holes (PBHs) are known as one of the potential candidates for dark matter. They are expected to have formed due to the direct gravitational collapse of density fluctuations in the early Universe. Therefore, the study of the merger rate of PBHs in modified theories of gravity can provide more detailed information about their abundance. In this work, we delve into the calculation of the merger rate of PBHs within the theoretical framework of $f(R)$ gravity. Our analysis reveals an enhancement in the merger rate of PBHs compared to that obtained from general relativity (GR). Additionally, modulating the field strength $f_{R0}$ induces shifts in the PBH merger rate, presenting a potential observational signature of modified gravity. We also find that the total merger rate of PBHs will be consistent with the merger rate of black holes estimated by the Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo-KAGRA detectors if $f_{PBH}\gtrsim 0.1$. While further improvements might be required, relative enhancement of the merger rate of PBHs in the framework of $f(R)$ gravity and its consistency with gravitational wave data underscore the importance of employing modified theories of gravity to examine diverse scenarios related to the formation of black holes.