Quantum Correlators in Friedmann Spacetimes -The omnipresent de Sitter and the invariant vacuum noise

TL;DR

This paper explores quantum field theory in Friedmann and de Sitter spacetimes, revealing mappings, integral representations, divergence phenomena, and a covariant approach to vacuum fluctuation spectra, enhancing understanding of quantum effects in cosmological backgrounds.

Contribution

It introduces a mapping between massless scalar fields in power-law universes and massive fields in de Sitter space, and develops a covariant method for analyzing vacuum fluctuations across different coordinate systems.

Findings

Mapping of scalar field dynamics between universes and de Sitter space

Integral representation of Euclidean Green's function via electrostatic analogy

Divergence of Wightman function in Friedmann universes with negative pressure

Abstract

We discuss several aspects of quantum field theory of a scalar field in a Friedmann universe, clarifying and highlighting several conceptual and technical issues. (A) We show that one can map the dynamics of (1) a massless scalar field in a universe with power law expansion to (2) a massive scalar field in the de Sitter spacetime, which allows us to understand several features of either system and clarifies several issues related to the massless limit. (B) We obtain a useful integral representation for the Euclidean Green's function for the de Sitter spacetime, by relating it to the solution of a hypothetical electrostatic problem in five dimensions. This is helpful in the study of several relevant limits. (C) We recover that in any Friedmann universe, sourced by a negative pressure fluid, the Wightman function for a massless scalar field is divergent. This shows that the divergence of Wightman function for the massless field in the de Sitter spacetime is just a special, limiting, case of this general phenomenon. (D) We provide a generally covariant procedure for defining the power spectrum of vacuum fluctuations in terms of the different Killing vectors present in the spacetime. This allows one to study the interplay of the choice of vacuum state and the nature of the power spectrum in different coordinate systems, in the de Sitter universe, in a unified manner. (Truncated Abstract; see the paper for full Abstract.)