Entanglement Entropy of Cosmological Perturbations

TL;DR

This paper explores how quantum vacuum fluctuations during early universe inflation generate entanglement entropy through mode interactions, impacting decoherence and placing bounds on inflation duration.

Contribution

It introduces a novel perspective linking cosmological perturbation entropy to momentum space entanglement and derives bounds on inflation duration from entropy considerations.

Findings

Entanglement entropy from nonlinear interactions dominates over vacuum squeezing entropy.

Decoherence of super-Hubble modes is caused by mode interactions.

Upper bound on inflation duration consistent with Trans-Planckian Censorship Conjecture.

Abstract

We show that the entropy of cosmological perturbations originating as quantum vacuum fluctuations in the very early universe, including the contribution of the leading nonlinear interactions, can be viewed as momentum space entanglement entropy between sub- and super-Hubble modes. The interactions between these modes causes decoherence of the super-Hubble fluctuations which, in turn, leads to a non-vanishing entropy of the reduced density matrix corresponding to the super-Hubble inhomogeneities. In particular, applying this to inflationary cosmology reveals that the entanglement entropy produced by leading order nonlinearities dominates over that coming from the squeezing of the vacuum state unless inflation lasts for a very short period. Furthermore, demanding that this entanglement entropy be smaller than the thermal entropy at the beginning of the radiation phase of standard cosmology leads to an upper bound on the duration of inflation which is similar to what is obtained from the Trans-Planckian Censorship Conjecture.