Numerically modeling stochastic inflation in slow-roll and beyond

Understand

We present a complete numerical treatment of inflationary dynamics under the influence of stochastic corrections from sub-Hubble modes.

• We discuss how to exactly model the stochastic noise terms arising from the sub-Hubble quantum modes that give rise to the coarse-grained inflaton dynamics in the form of stochastic differential equations.
• The stochastic differential equations are solved event-by-event on a discrete time grid.
• We then compute the power spectrum of curvature perturbations that can be compared with the power spectrum computed in the traditional fashion using the Mukhanov-Sasaki equation by canonically quantizing the inflaton fluctuations.