Tall tales from de Sitter space I: Renormalization group flows

TL;DR

The paper investigates homogeneous, asymptotically de Sitter spacetimes with a positive cosmological constant and scalar matter, focusing on the tallness of conformal diagrams and the dS/CFT interpretation as renormalization group flows. It introduces two solution-generation methods (pre-potential and step-potentials) to construct explicit asymptotically dS flows, and defines a generalized c-function Λ_eff that monotically tracks the flow under expansion or contraction. A generalized de Sitter c-theorem is proven (under mild energy conditions) for isotropic and some anisotropic foliations, and the global causal structure is explored via conformal diagrams for flat, spherical, and hyperbolic slices. The work then demonstrates the possibility of very tall, big-wide universes with arbitrarily large intermediate volumes, analyzes entropy bounds in such setups, and discusses the distinct roles of accessible versus available degrees of freedom in the dS/CFT framework. Overall, the paper extends the dS/CFT RG thermodynamics to a broader class of asymptotically dS spacetimes and clarifies the global and holographic implications of tall universes.

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.