Spacelike Fluctuations of the Stress Tensor for de Sitter Vacuum

TL;DR

This paper computes the two-point function of stress tensor fluctuations for a massless field in de Sitter space, showing these fluctuations are significant and could influence spacetime geometry and cosmological structure formation.

Contribution

It provides an explicit calculation of the spacelike two-point function of stress tensor fluctuations in de Sitter space, highlighting their importance for spacetime and cosmological fluctuations.

Findings

Stress tensor fluctuations are as significant as the expectation value.

Fluctuations can induce metric perturbations in de Sitter spacetime.

Results are relevant for understanding large-scale structure formation.

Abstract

The two-point function characterizing the stress tensor fluctuations of a massless minimally coupled field for an invariant vacuum state in de Sitter spacetime is discussed. This two-point function is explicitly computed for spacelike separated points which are geodesically connected. We show that these fluctuations are as important as the expectation value of the stress tensor itself. These quantum field fluctuations will induce fluctuations in the geometry of de Sitter spacetime. This paper is a first step towards the computation of such metric fluctuations, which may be of interest for large-scale structure formation in cosmology. The relevance of our results in this context is briefly discussed.