On the hologram of de Sitter

Abstract

A careful reduction of 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 made explicit. Space-times which correspond to nonequivalent profiles of the Liouville field at ${\mathcal{I}}^{\ensuremath{-}}$ and ${\mathcal{I}}^{+}$ are shown to exist. The qualitative implications of this for any tentative dual theory are presented.