Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity

TL;DR

This paper extends semiclassical gravity to include stochastic correlations, demonstrating how quantum fluctuations during inflation produce an almost-scale-invariant power spectrum and providing a basis for analyzing non-Gaussianities.

Contribution

It introduces an extended semiclassical Einstein equation framework coupling n-point functions, enabling detailed analysis of quantum fluctuations during inflation.

Findings

Produced an almost-scale-invariant power spectrum of scalar perturbations.

Provided a natural basis for calculating non-Gaussianities.

Applied the model to a massive conformally coupled scalar field on perturbed de Sitter space.

Abstract

We present an extension of the semiclassical Einstein equations which couples n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.