The Trouble with de Sitter Space

TL;DR

The authors investigate whether de Sitter space with finite horizon entropy can realize exact de Sitter symmetry within a thermofield-dynamics framework. They prove a no-go result: finite entropy implies a discrete spectrum that is incompatible with the patch-mixing symmetry generators, suggesting that either entropy must be infinite or patch symmetry must be broken. They discuss nonperturbative anomalies, Poincaré recurrences, and KKLT-style metastability as routes that preclude eternal de Sitter behavior. The work argues that physically meaningful de Sitter-like phases must involve either infinite entropy or symmetry breaking between causal patches, with recurrences and lifetimes constrained by these dynamics.

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.

Figures (1)

• Figure 1: Penrose diagrams for Minkowski space (on the left) and de Sitter space or the eternal anti-de Sitter black hole (on the right).