Stress tensor fluctuations in de Sitter spacetime

TL;DR

This paper calculates the stress tensor two-point function in de Sitter spacetime for various dimensions, revealing long-range correlations for light fields and a discontinuity at zero mass, with a new geometric interpretation of bitensors.

Contribution

It provides explicit formulas for stress tensor correlations in de Sitter space for arbitrary dimensions and masses, including a novel geometric interpretation of bitensors.

Findings

Long-range correlations for light fields with inverse power decay.

Discontinuity in the decay behavior at zero mass.

New geometric interpretation of de Sitter-invariant bitensors.

Abstract

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m^2/H^2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.