How Likely are Constituent Quanta to Initiate Inflation?

TL;DR

This paper introduces a framework to evaluate the likelihood of inflation starting in the early universe based on initial quantum conditions, concluding that such initiation at sub-Planckian densities is highly improbable.

Contribution

It presents a novel probabilistic approach to initial conditions in inflation, avoiding reliance on self-reproduction, and quantifies the low probability of inflation onset at sub-Planckian densities.

Findings

Inflation initiation probability at sub-Planckian densities is extremely low.

Regions that begin inflating below the self-reproductive threshold occupy negligible volume today.

Most of the universe's volume is from regions that never experienced inflation.

Abstract

We propose an intuitive framework for studying the problem of initial conditions in slow-roll inflation. In particular, we consider a universe at high, but sub-Planckian energy density and analyze the circumstances under which it is plausible for it to become dominated by inflated patches at late times, without appealing to the idea of self-reproduction. Our approach is based on defining a prior probability distribution for the constituent quanta of the pre-inflationary universe. To test the idea that inflation can begin under very generic circumstances, we make specific -- yet quite general and well grounded -- assumptions on the prior distribution. As a result, we are led to the conclusion that the probability for a given region to ignite inflation at sub-Planckian densities is extremely small. Furthermore, if one chooses to use the enormous volume factor that inflation yields as an appropriate measure, we find that the regions of the universe which started inflating at densities below the self-reproductive threshold nevertheless occupy a negligible physical volume in the present universe as compared to those domains that have never inflated.