Tall tales from de Sitter space I: Renormalization group flows

TL;DR

This paper explores the properties of tall universes in de Sitter space, their implications for the dS/CFT correspondence, and the associated renormalization group flows, including a generalized de Sitter c-theorem.

Contribution

It introduces a detailed analysis of tall universes, their large-volume Cauchy surfaces, and connects these to RG flows and a generalized de Sitter c-theorem.

Findings

Tall universes can have arbitrarily large volume for fixed asymptotic behavior.

Contracting phases correspond to IR flows, expanding phases to reverse UV flows.

The study extends the dS/CFT correspondence with a broader RG flow framework.

Abstract

We study solutions of Einstein gravity coupled to a positive cosmological constant and matter, which are asymptotically de Sitter and homogeneous. Regarded as perturbations of de Sitter space, a theorem of Gao and Wald implies that generically these solutions are `tall,' meaning that the perturbed universe lives through enough conformal time for an entire spherical Cauchy surface to enter any observer's past light cone. Such observers will realize that their universe is spatially compact. An interesting fact, which we demonstrate with an explicit example, is that this Cauchy surface can have arbitrarily large volume for fixed asymptotically de Sitter behavior. Our main focus is on the implications of tall universes for the proposed dS/CFT correspondence. Particular attention is given to the associated renormalization group flows, leading to a more general de Sitter `c-theorem.' We find, as expected, that a contracting phase always represents a flow towards the infrared, while an expanding phase represents a `reverse' flow towards the ultraviolet. We also discuss the conformal diagrams for various classes of homogeneous flows.