Black hole production, eternal inflation, and information in quasi-de Sitter space

TL;DR

This paper explores conditions under which eternal inflation occurs in quasi-de Sitter space, analyzing black hole formation, information paradox implications, and the role of density fluctuations and degrees of freedom.

Contribution

It introduces a novel connection between radiation density fluctuations, black hole formation, and the no eternal inflation condition in quasi-de Sitter space.

Findings

Eternal inflation occurs when $\epsilon_H < H^2/M_{Pl}^2$.

Black hole production is suppressed if radiation fluctuations are below a certain threshold.

The information paradox is avoided for specific parameter ranges, supporting complementarity.

Abstract

When the slow-roll parameter $\epsilon_H$ is smaller than $H^2/M_{\rm Pl}^2$, the quantum fluctuations of the inflaton after the horizon crossing are large enough to realize eternal inflation. Whereas they do not generate a sufficient amount of density fluctuation of the inflaton to produce the black hole in quasi-de Sitter space, they can also generate the sizeable density fluctuation of the radiation when the number of degrees of freedom increases rapidly in time, as predicted by the distance conjecture. We argue that the condition that the density fluctuation of the radiation is not large enough to produce the black hole until the end of inflation is equivalent to the no eternal inflation condition. When the radiation emitted by the horizon does not produce the black hole, even if the number of degrees of freedom increases in time, the information paradox does not arise for $\epsilon_H$ larger than $10^{-7} (H^2/ M_{\rm Pl}^2)$ and time scale shorter than $10^4 (M_{\rm Pl}/H^2)$. Regardless of the presence of the information paradox, a static observer cannot retrieve a sufficient amount of information, which is consistent with the complementarity.