Future Foam

TL;DR

This paper explores the possible boundary topologies of pocket universes in eternal inflation, demonstrating that boundaries of any genus can occur and discussing implications for holographic dual descriptions.

Contribution

It introduces simplified models to show the existence of boundaries with arbitrary genus in pocket universes and discusses their implications for holographic duality in eternal inflation.

Findings

Boundaries of any genus can occur in pocket universes.

Existence of geometries with a single toroidal boundary.

Multiple disconnected boundaries can also occur.

Abstract

We study pocket universes which have zero cosmological constant and non-trivial boundary topology. These arise from bubble collisions in eternal inflation. Using a simplified dust model of collisions we find that boundaries of any genus can occur. Using a radiation shell model we perform analytic studies in the thin wall limit to show the existence of geometries with a single toroidal boundary. We give plausibility arguments that higher genus boundaries can also occur. In geometries with one boundary of any genus a timelike observer can see the entire boundary. Geometries with multiple disconnected boundaries can also occur. In the spherical case with two boundaries the boundaries are separated by a horizon. Our results suggest that the holographic dual description for eternal inflation, proposed by Freivogel, Sekino, Susskind and Yeh, should include summation over the genus of the base space of the dual conformal field theory. We point out peculiarities of this genus expansion compared to the string perturbation series.