Rest frame vacua of massive Klein-Gordon fields on spatially flat FLRW spacetimes

TL;DR

This paper introduces a method to project quantum states between different geometries in flat FLRW spacetimes, defining a rest frame vacuum for massive scalar fields and analyzing its stability and particle creation effects.

Contribution

It presents a novel approach for defining and analyzing rest frame vacua in flat FLRW spacetimes, including stability analysis and particle creation phenomena.

Findings

The rest frame vacuum is stable in de Sitter universe.

In Milne-type spacetimes, the vacuum is dynamic and leads to early universe particle creation.

The method allows for consistent measurement of Minkowskian parameters in curved spacetimes.

Abstract

We propose a method of projecting the quantum states from a state space of a given geometry into another state space generated by a different geometry, taking care on the correct normalization which is crucial in interpreting the quantum theory. Thanks to this method we can define on any spatially flat FLRW spacetime states in which genuine Minkowskian parameters are measured. We use these Minkowskian states for separating the frequencies in the rest frames of the massive scalar particles defining thus the scalar rest frame vacuum. We show that this vacuum is stable on the de Sitter expanding universe where the energy is conserved. In contrast, on a spatially flat FLRW spacetime with a Milne-type scale factor this vacuum results to be dynamic, corresponding to a time-dependent rest energy interpreted as an effective mass. This dynamic vacuum give rise to a cosmological particle creation which is significant only in the early Milne-type universe considered here. Some interesting features of this new effect are pointed out in a brief analysis.