Stochastic growth of quantum fluctuations during inflation

TL;DR

This paper introduces a stochastic approach to analyze quantum fluctuations during slow-roll inflation, showing how the growth of fluctuations depends on the inflationary model and effective mass of fields.

Contribution

It demonstrates the necessity of using the logarithm of the scale factor as the time variable in the stochastic Fokker-Planck equation for accurate fluctuation growth calculations.

Findings

Quantum fluctuations grow faster than test fields with non-negative mass in most models.

The growth rate differs notably in hybrid inflation models.

The approach clarifies the relation between gauge-invariant fluctuations and stochastic dynamics.

Abstract

The standard field-theoretical approach to the slow-roll inflation is introduced. We then show as, in order to calculate the mean square of the canonical gauge invariant quantum fluctuations associated to a generic field, the logarithm of the scale factor has to be used as the time variable in the Fokker-Planck equation in the stochastic approach. Then we compute the growth of different test fields with a small effective mass during slow-roll inflationary models, comparing the results with the one for the gauge invariant canonical fluctuation associated to the inflaton, the Mukhanov variable. We find that in most of the single fields inflationary models such fluctuation grows faster than any test field with a non-negative effective mass, with the exception of hybrid models.