Tall tales from de Sitter space I: Renormalization group flows

We study solutions of Einstein gravity coupled to a positive cosmologicalconstant and matter, which are asymptotically de Sitter and homogeneous.Regarded as perturbations of de Sitter space, a theorem of Gao and Wald impliesthat generically these solutions are `tall,' meaning that the perturbeduniverse lives through enough conformal time for an entire spherical Cauchysurface to enter any observer's past light cone. Such observers will realizethat their universe is spatially compact. An interesting fact, which wedemonstrate with an explicit example, is that this Cauchy surface can havearbitrarily large volume for fixed asymptotically de Sitter behavior. Our mainfocus is on the implications of tall universes for the proposed dS/CFTcorrespondence. Particular attention is given to the associated renormalizationgroup flows, leading to a more general de Sitter `c-theorem.' We find, asexpected, that a contracting phase always represents a flow towards theinfrared, while an expanding phase represents a `reverse' flow towards theultraviolet. We also discuss the conformal diagrams for various classes ofhomogeneous flows.Comment: 32 pages, 16 figures, references adde