Stochastic inflation and entropy bound in de Sitter spacetime

TL;DR

This paper explores the entropy dynamics in de Sitter spacetime during inflation, revealing violations of the entropy bound and proposing a stochastic approach to analyze the entropy behavior of the inflaton field.

Contribution

It introduces a stochastic inflation framework to study entropy bounds, linking quantum information concepts with cosmological horizon entropy during inflation.

Findings

Entropy bound violations occur during eternal inflation.

Shannon entropy of the inflaton field reflects entanglement entropy behavior.

Volume-weighted probability distribution reveals significant entropy dynamics.

Abstract

We investigate the entropy dynamics of de Sitter spacetime during the inflationary phase. The cosmological horizon in de Sitter spacetime, which limits the causally accessible region for an observer, exhibits thermal properties similar to a black hole event horizon. According to holographic principles, the entropy within a causally connected region is bounded by its surface area. However, this entropy bound is violated during the eternal phase of inflation. To address these violations from a quantum information perspective, we adopt a stochastic approach to cosmic inflation. Specifically, we analyze the Shannon entropy of the inflaton field's probability distribution, which mirrors the behavior of the entanglement entropy of a Hubble-sized region in stochastic inflation. Using the volume-weighted probability distribution for the inflaton field, we demonstrate a significant entropy behavior in de Sitter spacetime.