Effect of Inhomogeneity on Primordial Black Hole Formation in the Matter Dominated Era

TL;DR

This paper studies how inhomogeneity and finite information propagation speed during the matter era influence primordial black hole formation, revealing a significantly increased formation probability compared to previous models assuming instantaneous information transfer.

Contribution

It introduces a new threshold criterion for black hole formation considering finite information speed, leading to a higher predicted formation probability in the matter dominated era.

Findings

Black hole formation probability is significantly enhanced with finite information propagation speed.

Derived a new probability formula: $eta_{inhom} oughly 3.70 \sigma^{3/2}$ for small $\sigma$.

Shows that previous models underestimated black hole formation likelihood by assuming instantaneous information transfer.

Abstract

We investigate the effect of inhomogeneity on primordial black hole formation in the matter dominated era. In the gravitational collapse of an inhomogeneous density distribution, a black hole forms if apparent horizon prevents information of the central region of the configuration from leaking. Since information cannot propagate faster than the speed of light, we identify the threshold of the black hole formation by considering the finite speed for propagation of information. We show that the production probability $\beta_{inhom}(\sigma)$ of primordial black holes, where $\sigma$ is density fluctuation at horizon entry, is significantly enhanced from that derived in previous work in which the speed of propagation was effectively regarded as infinite. For $\sigma \ll 1$, we obtain $\beta_{inhom}\simeq 3.70 \sigma^{3/2}$, which is larger by about an order of magnitude than the probability derived in earlier work by assuming instantaneous propagation of information.