Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude

The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into the long-wavelength domain. The effective evolution may be derived from first principles quantum field theory in an expanding background, through a sequence of approximations calling for additional scrutiny. We perform such an analysis, putting particular emphasis on the amplitude of the stochastic noise, which ultimately determines the cosmological correlations and provides a non-perturbative IR regulator to the dynamics.