Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations

TL;DR

This paper develops a nonequilibrium quantum field theory framework to analyze the intrinsic entropy of squeezed quantum fields in cosmology, revealing quantum properties like entanglement and coherence that classical approaches overlook.

Contribution

It introduces a comprehensive quantum field-theoretic method to compute entropy of cosmological perturbations, highlighting quantum effects absent in classical stochastic models.

Findings

Entropy of the closed system is zero, but particle production leads to non-zero entropy after coarse-graining.

Quantum entanglement and coherence are captured, unlike in classical stochastic treatments.

The approach bridges quantum field theory and classical stochastic descriptions, emphasizing quantum advantages.

Abstract

Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, as different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using probability distribution of classical stochastic fields by earlier authors. From this we can see the clear advantages of the quantum field-theoretical approach over the stochastic classical field treatment since the latter misses out in some important quantum properties, such as entanglement and coherence, of the quantum field.