Cosmological production of black holes: a way to constrain alternative theories of gravity

TL;DR

This paper investigates primordial black hole production during inflation within alternative gravity theories, proposing that such theories should exhibit black hole creation rates similar to General Relativity, and uses this to constrain $f(R)$ models.

Contribution

It introduces a criterion for black hole production rates in alternative gravity theories based on quantum cosmology and applies it to constrain parameters in $f(R)$-theories.

Findings

Black hole creation rate in alternative theories should mirror that of GR.

Derived a general formula for $f(R)$-theories with constant curvature.

Placed constraints on parameters of well-known $f(R)$-models.

Abstract

Primordial black holes are considered to be pair created quantum-mechanically during inflation. In the context of General Relativity (GR), it has been shown that the pair creation rate is exponentially decreasing during inflation. Specifically, tiny black holes are favored in the early universe, but they can grow with the horizon scale, as inflation approaches its end. At the same time, cosmological, and not only, shortcomings of GR have triggered the pursuit for a new, alternative theory of gravity. In this paper, by using probability amplitudes from the No Boundary Proposal (NBP), we argue that any alternative gravity should have a black hole creation rate similar to that of GR; that is, in the early universe the creation of small black holes is in favor, while in the late universe larger black holes are being exponentially suppressed. As an example, we apply this argument in $f(R)$-theories of gravity and derive a general formula for the rate in any $f(R)$-theory with constant curvature. Finally, we consider well known $f(R)$-models and using this formula we put constraints in their free parameters.