Gaussian state for the bouncing quantum cosmology

TL;DR

This paper investigates how Gaussian quantum states evolve through the cosmological bounce in loop quantum cosmology, demonstrating preservation of semiclassicality and introducing entropy of squeezing as an evolution parameter.

Contribution

It applies reduced phase space quantization to analyze Gaussian state propagation across the bounce, revealing minimal quantum effects at the bounce and proposing entropy of squeezing as an evolution indicator.

Findings

Gaussian state is least quantum at the bounce

Semiclassicality is preserved across the bounce

Entropy of squeezing aligns with von Neumann entropy predictions

Abstract

We present results concerning propagation of the Gaussian state across the cosmological quantum bounce. The reduced phase space quantization of loop quantum cosmology is applied to the Friedman-Robertson-Walker universe with a free massless scalar field. Evolution of quantum moments of the canonical variables is investigated. The covariance turns out to be a monotonic function so it may be used as an evolution parameter having quantum origin. We show that for the Gaussian state the Universe is least quantum at the bounce. We propose explanation of this counter-intuitive feature using the entropy of squeezing. The obtained time dependence of entropy is in agreement with qualitative predictions based on von Neumann entropy for mixed states. We show that, for the considered Gaussian state, semiclassicality is preserved across the bounce, so there is no cosmic forgetfulness.