Non-Gaussian Stochastic Gravity

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.