Unitary and non-unitary transitions around a cosmological bounce

TL;DR

This paper explores how to define time and unitarity near a cosmological bounce in quantum cosmology, proposing the use of matter conjugate momentum as a time parameter to ensure consistent probabilities.

Contribution

It introduces a novel approach using matter conjugate momentum as time to analyze transitions around a cosmological bounce, overcoming WKB limitations.

Findings

Conditions for recovering unitarity near a bounce

Explicit computation of matter transitions in a bouncing universe

Highlighting the importance of conjugate momentum for beyond-background analysis

Abstract

In this work, we investigate the notion of time and unitarity in the vicinity of a bounce in quantum cosmology, that is, a turning point for the scale factor. Because WKB methods drastically fail near a turning point, the scale factor cannot play the role of time in such scenarios. We overcome this difficulty by studying the dynamics of matter transitions when using its conjugate momentum as a time. We find precise conditions so as to recover unitarity, and hence, a consistent notion of probability. We then compute transitions in a concrete example, extract the specific feature of a bounce and argue about the necessity of the conjugate momentum representation to go beyond the background field approximation. Our analysis is also equally relevant for a closed Universe undergoing a recollapsing phase.