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

Abstract

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.

Primordial black holes and stochastic inflation beyond slow roll. Part I. Noise matrix elements

“…This assumption has been questioned, especially because the sharp cut-off window function may not lead to well-behaved coarse-grained field correlators in the physical space. See refs [73,88,89]. for more discussion.…”