On the Phase-Space Volume of Primordial Cosmological Perturbations

TL;DR

This paper derives an invariant measure of phase space volume for primordial gravitational waves during inflation, revealing that the quasi-classical entropy of the initial vacuum state remains zero despite fluctuation generation.

Contribution

It introduces a method to compute the phase space volume of primordial perturbations that is invariant under squeezing transformations during inflation.

Findings

Derived an expression for phase space volume in the long wavelength regime.

Showed that the quasi-classical entropy of the vacuum remains zero.

Demonstrated invariance of phase space volume under squeezing transformations.

Abstract

We show how to determine the typical phase space volume $\Gamma$ for primordial gravitational waves produced during an inflationary stage, which is invariant under squeezing. An expression for $\Gamma$ is found in the long wavelength regime. The quasi-classical entropy of a pure vacuum initial state defined as the logarithm of $\Gamma$ modulo a constant remains zero in spite of the generation of fluctuations (creation of real gravitons).