Exact noise kernel for quantum fields in static de Sitter and conformally-flat spacetimes

TL;DR

This paper provides exact formulas for the noise kernel of conformally-invariant scalar fields in static de Sitter and conformally-flat spacetimes, offering insights into quantum fluctuations near horizons and validating approximation methods.

Contribution

It derives explicit exact expressions for the noise kernel in conformally-flat spacetimes and analyzes their behavior near horizons, improving understanding of quantum field fluctuations in these backgrounds.

Findings

Exact noise kernel expressions for conformally-invariant scalar fields.

Analysis of noise kernel behavior near the cosmological horizon.

Validation of quasi-local approximation near horizons.

Abstract

We compute exact expressions of the noise kernel, defined as the expectation value of the symmetrized connected stress energy bitensor, for conformally-invariant scalar fields with respect to the conformal vacuum, valid for an arbitrary separation (timelike, spacelike and null) of points in a class of conformally-flat spacetimes. We derive explicit expressions for the noise kernel evaluated in the static de Sitter coordinates with respect to the Gibbons-Hawking vacuum and analyze the behavior of the noise kernel in the region near the cosmological horizon. We develop a quasi-local expansion near the cosmological horizon and compare it with the exact results. This gives insight into the likely range of validity of the quasi-local approximation expressions for the noise kernel for the conformally invariant scalar field in Schwarzschild spacetime which are given in PHYSICAL REVIEW D{\bf 85}, 044037 (2012).