Universality of the Volume Bound in Slow-Roll Eternal Inflation

TL;DR

This paper demonstrates that the volume bound in slow-roll eternal inflation is universal across dimensions and models, linking it to de Sitter entropy and providing a formalism for volume distribution analysis.

Contribution

It proves the universality of the volume bound in slow-roll inflation across different dimensions and multi-field scenarios, and introduces a formalism for volume distribution computation.

Findings

The volume bound holds universally in various dimensions and models.

The bound is saturated at the transition to eternal inflation.

A formalism for volume distribution in multi-field models is provided.

Abstract

It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than e^(S_dS/2) without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic interpretation. As a spin-off we provide the formalism to compute the probability distribution of the volume after inflation for generic multi-field models, which might help to address questions about the population of vacua of the landscape during slow-roll inflation.