Stochastic growth of quantum fluctuations during inflation

Understand

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.