Abstract

I discuss recent work with Bobev and Vreys which is motivated by holography, both with AdS and with de Sitter boundary conditions. In this, we first evaluate the partition function of the free O(N) vector model on a two-parameter family of squashed three spheres. We then obtain generalisations of the AdS Taub-NUT and Taub-Bolt solutions of Einstein gravity with the same double squashed boundary geometries. Remarkably, both systems exhibit a qualitatively similar behaviour over the entire configuration space of boundary geometries.

Recent formulations of dS/CFT enable one to interpret the partition function as a function of the two squashing parameters as the Hartle-Hawking wave function in a minisuperspace model of anisotropic deformations of de Sitter space. I discuss the resulting probability distribution over histories in this model and argue that for the probabilities to be well defined one must restrict to future boundary configurations corresponding to stable deformations of the field theory. I conjecture this restriction implies the exit from scalar field driven eternal inflation is reasonably smooth in holographic cosmology.