Quantum Stress Tensor Fluctuations and their Physical Effects

Abstract

We summarize several aspects of recent work on quantum stress tensor fluctuations and their role in driving fluctuations of the gravitational field. The role of correlations and anticorrelations is emphasized. We begin with a review of the properties of the stress tensor correlation function. We next consider some illuminating examples of non-gravitational effects of stress tensors fluctuations, specifically fluctuations of the Casimir force and radiation pressure fluctuations. We next discuss passive fluctuations of spacetime geometry and some of their operational signatures. These include luminosity fluctuations, line broadening, and angular blurring of a source viewed through a fluctuating gravitational field. Finally, we discuss the possible role of quantum stress tensor fluctuations in the early universe, especially in inflation. The fluctuations of the expansion of a congruence of comoving geodesics grows during the inflationary era, due to non-cancellation of anticorrelations that would have occurred in flat spacetime. This results in subsequent non-Gaussian density perturbations and allows one to infer an upper bound on the duration of inflation. This bound is consistent with adequate inflation to solve the horizon and flatness problems.

Cosmological bounds on TeV-scale physics and beyond

“…Vacuum stress-energy fluctuations -in particular two-point correlators -have been studied in a flat space context [8] as well as on curved space [9,10], including de Sitter space [11,12] and inflation [13]. The physical effects of stress tensor fluctuations on the gravitational field were reviewed in [14]. We also note that our results -in particular Section VI -share some overlap with results in stochastic gravity (see [15] and references therein).…”

Spacetime foam: a review

“…Until recently, though, most of this work focused on small fluctuations that could be treated at low order in perturbation theory. Such fluctuations can have interesting physical effects-see, for instance, [114]but they are not really spacetime foam. Over the past few years, however, a good deal of progress has been made in understanding high order stress-energy correlators and large fluctuations, leading to something much closer to Wheeler's original conception [115][116][117][118].…”

“…will still have divergences, which will in general be statedependent [114]. These remaining divergences can be eliminated by integrating :T µν : against a sampling (or 'smearing') function [120],…”

Pulsar Timing Constraints on Physics Beyond the Standard Model

“…where we have explicitly denoted the connected contribution from zero-point vacuum fluctuations, and the LHS is the contribution to Einstein tensor fluctuations from matter in the vacuum. Such gravitational effects from vacuum fluctuations have been reviewed in [3] (see also [4,5]), and in the stochastic gravity formalism [6].…”