The Thermodynamics of Cosmological Horizons and Their Holographic Description in de Sitter Space

TL;DR

This paper explores the thermodynamics of cosmological horizons in de Sitter space and their holographic dual, establishing a universal first law and defining entropy via boundary charges.

Contribution

It introduces a universal first law for cosmological horizons in de Sitter space and defines a boundary-based entropy in the holographic dual.

Findings

Universal form of the first law of thermodynamics for de Sitter horizons

Entropy defined on a boundary surface as a function of boundary charges

Analysis of the second law and holographic implications in de Sitter space

Abstract

We analyse the laws of thermodynamics governing the behaviour of cosmological horizons in de Sitter space and their map to a holographic description at future infinity, $\mathcal{I}^+$. In this case, the boundary can receive signals from two cosmological horizons. We find a universal form for the first law of thermodynamics, valid in general circumstances, when matter-energy crosses both horizons and impinges on the boundary. This universal form leads to a well defined notion of entropy in the holographic dual. It is specified on a co-dimension one surface of the boundary, and can be expressed as a function of two boundary charges, pressure and angular momentum, both of which are derived from the Brown-York stress tensor. Additional comments on the second law, confusing factors of $i$ which arise, and comments pertaining to JT gravity, are included towards the end.