The Trouble with de Sitter Space

TL;DR

This paper examines the implications of finite entropy and symmetry in de Sitter space, proving a no-go theorem that constrains the possible long-term behavior of de Sitter phases and their relation to quantum gravity.

Contribution

It presents a no-go theorem showing that symmetries cannot be exactly implemented if de Sitter entropy is finite, impacting the understanding of de Sitter space in quantum gravity.

Findings

Finite entropy implies symmetry implementation issues.

De Sitter phase lifetime is limited by Poincare recurrence time.

Supports the idea that de Sitter space cannot have exact classical symmetries.

Abstract

In this paper we assume the de Sitter Space version of Black Hole Complementarity which states that a single causal patch of de Sitter space is described as an isolated finite temperature cavity bounded by a horizon which allows no loss of information. We discuss the how the symmetries of de Sitter space should be implemented. Then we prove a no go theorem for implementing the symmetries if the entropy is finite. Thus we must either give up the finiteness of the de Sitter entropy or the exact symmetry of the classical space. Each has interesting implications for the very long time behavior. We argue that the lifetime of a de Sitter phase can not exceed the Poincare recurrence time. This is supported by recent results of Kachru, Kallosh, Linde and Trivedi.