Quantum linear scalar fields with time dependent potentials: Overview and applications to cosmology

TL;DR

This paper reviews recent results on the unique quantization of scalar fields in various cosmological spacetimes, emphasizing symmetry and unitarity criteria to resolve quantization ambiguities and identify preferred variables.

Contribution

It provides a comprehensive overview of the criteria used to achieve unique and physically meaningful quantizations of scalar fields in cosmological models.

Findings

Uniqueness results for scalar field quantization in cosmological spacetimes

Criteria of symmetry invariance and unitarity effectively resolve quantization ambiguities

Identification of preferred variables for scalar field quantization in cosmology

Abstract

In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lema\^{\i}tre-Robertson-Walker, de Sitter, and Bianchi I spacetimes. These results are attained by imposing the criteria of symmetry invariance and of unitary implementability of the dynamics. This powerful combination of criteria allows not only to address the ambiguity in the representation of the canonical commutation relations, but also to single out a preferred set of fundamental variables. For the sake of clarity and completeness in the presentation (essentially as a background and complementary material), we first review the classical and quantum theories of a scalar field in globally hyperbolic spacetimes. Special emphasis is made on complex structures and the unitary implementability of symplectic transformations.