Non-Gaussian Stochastic Gravity

TL;DR

This paper introduces a non-Gaussian approach to stochastic gravity, incorporating higher moments of quantum stress energy fluctuations, revealing a shifted Gamma distribution with a negative cutoff and a high probability of negative energy density in Minkowski space.

Contribution

It develops a novel non-Gaussian formulation of stochastic gravity that includes higher moments of quantum stress energy fluctuations and characterizes their probability distribution.

Findings

Fluctuations follow a shifted Gamma distribution.

Energy density has a negative cutoff at a small negative value.

Approximately 62% probability of negative energy density.

Abstract

This paper presents a new, non-Gaussian formulation of stochastic gravity by incorporating the higher moments of the fluctuations of the quantum stress energy tensor for a free quantum scalar field in a consistent way. A scheme is developed for obtaining realizations of these fluctuations in terms of the Wightman function, and the behavior of the fluctuations is investigated. The resulting probability distribution for fluctuations of the energy density in Minkowski spacetime is found to be similar to a shifted Gamma distribution. This distribution features a minimum energy density cutoff at a small negative value, but a sharp peak in the vicinity of this cutoff such that the total probability of observing a negative value is approximately 62%, balanced by correspondingly larger but rarer positive values.