Dwelling on de Sitter

TL;DR

This paper reduces three-dimensional gravity to a Liouville theory in asymptotic de Sitter spaces, exploring the roles of infinities and the implications for dual theories.

Contribution

It provides a detailed reduction of 3D gravity to Liouville theory with conditions from asymptotic de Sitter spaces, highlighting new space-time profiles.

Findings

Existence of non-equivalent Liouville profiles at past and future infinities

Conditions on Liouville fields imposed by space-time evolution

Implications for dual theories in de Sitter space

Abstract

A careful reduction of the three-dimensional gravity to the Liouville description is performed, where all gauge fixing and on-shell conditions come from the definition of asymptotic de Sitter spaces. The roles of both past and future infinities are discussed and the conditions space-time evolution imposes on both Liouville fields are explicited. Space-times which correspond to non-equivalent profiles of the Liouville field at past and future infinities are shown to exist. The qualitative implications of this for any tentative dual theory are presented.