Cosmological Density Fluctuations in Stochastic Gravity -- Formalism and Linear Analysis --

TL;DR

This paper investigates primordial cosmological perturbations using stochastic gravity, comparing results with standard linear theory, and finds agreement on observable scales but discrepancies on superhorizon scales, indicating the need for extended quantization.

Contribution

It introduces a formalism for analyzing primordial perturbations in stochastic gravity and compares its predictions with gauge-invariant linear perturbation theory, highlighting the conditions for agreement and discrepancies.

Findings

Agreement with gauge-invariant theory for sub-horizon scales

Discrepancy on superhorizon scales suggests missing gravitational degrees of freedom

Highlights importance of including longitudinal gravitational modes in quantization

Abstract

We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon crossing time is smaller than some critical value ($\sim |$slow-roll parameter $|^{-1}$), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.