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.
Highlights
Class of diagrams [10,11,12]
In the simplest overdamped limit, φ 3Hφ, and in addition neglecting spatial gradients, the effective IR dynamics can be described by a Langevin equation, and field correlations be obtained via the corresponding Fokker-Planck equation
We have revisited the derivation of stochastic inflation from first-principles quantum field theory
Summary
We first briefly review the stochastic inflationary formalism, and how a dynamical mass is generated. For f = 1, this is the finite part of the field correlator in the Bunch-Davies vacuum at leading order in the limit m2 H2. √ The effective mass squared is proportional to H2 and importantly to λ, rather than an integer power of the coupling This non-analytic dependence suggests that the stochastic prescription amounts to a resummation of Feynman diagrams from all orders of perturbation theory, providing an IR regulator in an expanding background (H = 0). The Langevin dynamics can be written as two coupled equations for the IR field and its time derivative: φIR = πIR + ξφ, π IR + 3HπIR + V (φIR) = ξπ,.
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