No Page Curves for the de Sitter Horizon

TL;DR

This paper explores the entropy of the de Sitter horizon, revealing that while theoretical models suggest unitary evolution, practical backreaction prevents observing a true Page curve, challenging the understanding of de Sitter entropy.

Contribution

It introduces a partial reduction approach to study de Sitter entropy and applies the island formula, highlighting the limitations due to backreaction in realistic scenarios.

Findings

Future infinity observer sees a pure state

Static patch observer needs island formula for unitarity

Backreaction prevents actual unitary evaporation

Abstract

We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at future infinity and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the past cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at future infinity naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page time, and neither observer will see unitary evaporation.