Gauge - invariant fluctuations of the metric in stochastic inflation

TL;DR

This paper derives a gauge-invariant stochastic equation for metric perturbations during inflation, quantizes the associated field, and discusses the significance of these perturbations in the infrared sector for power-law expanding universes.

Contribution

It introduces a gauge-invariant stochastic framework for metric perturbations and develops a quantization method for these perturbations during inflation.

Findings

Derived stochastic equation for gauge-invariant metric perturbations

Quantized the field describing these perturbations

Highlighted importance of infrared sector in power-law inflation

Abstract

I derive the stochastic equation for the perturbations of the metric for a gauge - invariant energy - momemtum - tensor (EMT) in stochastic inflation. A quantization for the field that describes the gauge - invariant perturbations for the metric is developed. In a power - law expansion for the universe the amplitude for these perturbations on a background metric could be very important in the infrared sector.