Stochastic semiclassical gravity and fluctuations during inflation

TL;DR

This paper discusses stochastic semiclassical gravity, introducing Einstein-Langevin equations, and applies the theory to inflation, showing that quantum fluctuations induce scale-invariant gravitational fluctuations consistent with structure formation.

Contribution

It introduces the Einstein-Langevin equations for stochastic semiclassical gravity and demonstrates their application in inflationary models, linking quantum matter fluctuations to gravitational perturbations.

Findings

Gravitational fluctuations exhibit an almost scale-invariant spectrum.

The theory aligns with standard structure formation models.

Recent applications of the framework are summarized.

Abstract

Stochastic semiclassical gravity is a theory for the interaction of gravity with quantum matter fields which goes beyond the semiclassical limit. The theory predicts stochastic fluctuations of the classical gravitational field induced by the quantum fluctuations of the stress energy tensor of the matter fields. Here we use an axiomatic approach to introduce the Einstein-Langevin equations as the consistent set of dynamical equations for a first order perturbative correction to semiclassical gravity and review their main features. We then describe the application of the theory in a simple chaotic inflationary model, where the fluctuations of the inflaton field induce stochastic fluctuations in the gravitational field. The correlation functions for these gravitational fluctuations lead to an almost Harrison-Zel'dovich scale invariant spectrum at large scales, in agreement with the standard theories for structure formation. A summary of recent results and other applications of the theory is also given.