The grainy multiverse

TL;DR

This paper explores the complex topological structures of spacelike slices in eternal inflation landscapes with multiple vacua, revealing a rich phase diagram including novel tubular phases and a generic grainy phase.

Contribution

It introduces a generalized toy model for landscape topology, uncovering new phases and analyzing their properties in the context of eternal inflation.

Findings

Identification of novel tubular phases with crossing curves of specific vacua

Discovery of a democratic tubular phase with all vacua types

Most realistic landscapes end in a grainy phase with mixed vacua regions

Abstract

I consider a landscape containing three vacua and study the topology of global spacelike slices in eternal inflation. A discrete toy model, which generalizes the well studied Mandelbrot model, reveals a rich phase structure. Novel phases include monochromatic tubular phases, which contain crossing curves of only one vacuum, and a democratic tubular phase, which contains crossing curves of all three types of vacua. I discuss the generalization to realistic landscapes consisting of many vacua. Generically, the system ends up in a grainy phase, which contains no crossing curves or surfaces and consists of packed regions of different vacua. Other topological phases arise on the scale of several generations of nucleations.