A unique Fock quantization for fields in non-stationary spacetimes

TL;DR

This paper proves a stronger uniqueness result for Fock quantization of fields in non-stationary spacetimes, ensuring a single, physically consistent quantum description under broad conditions relevant to cosmology.

Contribution

It extends previous uniqueness results by showing that the Fock quantization remains unique even with linear time-dependent transformations of the field.

Findings

Uniqueness of Fock quantization persists under time-dependent field scalings.

Only one $SO(4)$-invariant Fock representation respects the probabilistic interpretation.

Results have significant implications for quantum field theory in cosmological models.

Abstract

In curved spacetimes, the lack of criteria for the construction of a unique quantization is a fundamental problem undermining the significance of the predictions of quantum field theory. Inequivalent quantizations lead to different physics. Recently, however, some uniqueness results have been obtained for fields in non-stationary settings. In particular, for vacua that are invariant under the background symmetries, a unitary implementation of the classical evolution suffices to pick up a unique Fock quantization in the case of Klein-Gordon fields with time-dependent mass, propagating in a static spacetime whose spatial sections are three-spheres. In fact, the field equation can be reinterpreted as describing the propagation in a Friedmann-Robertson-Walker spacetime after a suitable scaling of the field by a function of time. For this class of fields, we prove here an even stronger result about the Fock quantization: the uniqueness persists when one allows for linear time-dependent transformations of the field in order to account for a scaling by background functions. In total, paying attention to the dynamics, there exists a preferred choice of quantum field, and only one $SO(4)$-invariant Fock representation for it that respects the standard probabilistic interpretation along the evolution. The result has relevant implications e.g. in cosmology.