Quantum unitary dynamics in cosmological spacetimes

TL;DR

This paper investigates the conditions under which scalar field dynamics in cosmological spacetimes can be implemented unitarily, identifying a preferred quantization and clarifying the relation between different representations and the S-matrix.

Contribution

It establishes criteria for unitary evolution of scalar fields in cosmology, highlighting a preferred quantization and comparing different notions of unitarity.

Findings

Unitary evolution singles out a specific field rescaling and Fock representation.

A privileged quantization exists even when dynamics are not unitarily implementable for the unscaled field.

The S-matrix is well-defined in both rescaled and unscaled descriptions.

Abstract

We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.