Threshold of primordial black hole formation in Eddington-inspired-Born-Infeld gravity

TL;DR

This paper investigates how the threshold for primordial black hole formation varies in Eddington-inspired-Born-Infeld gravity, revealing dependence on the gravitational theory and energy scale, thus offering a potential test for alternative gravity models.

Contribution

It provides the first analytic estimation of PBH formation thresholds in Eddington-inspired-Born-Infeld gravity, highlighting the dependence on gravitational theory parameters and energy scales.

Findings

Threshold is enhanced with positive Born-Infeld coupling.

Threshold is suppressed with negative coupling.

Threshold depends on the universe's energy scale at formation.

Abstract

It is believed that primordial black holes (PBHs), if they exist, can serve as a powerful tool to probe the early stage of the cosmic history. Essentially, in the radiation dominated universe, PBHs could form by the gravitational collapse of overdense primordial perturbations produced during inflation. In this picture, one important ingredient is the threshold of density contrast, which defines the onset of PBH formation. In the literature, most of the estimations of threshold, no matter numerically or analytically, are implemented in the framework of general relativity (GR). In this paper, by performing analytic estimations, we point out that the threshold for PBH formation depends on the gravitational theory under consideration. In GR, given a fixed equation of state, the analytic estimations adopted in this paper give a constant value of the formation threshold. If the theory is characterized by additional mass scales other than the Planck mass, the estimated threshold of density contrast may depend on the energy scale of the universe at the time of PBH formation. In this paper, we consider the Eddington-inspired-Born-Infeld gravity as an example. We find that the threshold would be enhanced if the Born-Infeld coupling constant is positive, and would be suppressed for a negative coupling constant. Also, we show explicitly that the threshold depends on the energy scale of the universe at the PBH formation time. This conclusion is expected to be valid for any gravitational theory characterized by additional mass scales, suggesting the possibility of testing gravitational theories with PBHs.