Open EFTs, IR effects & late-time resummations: systematic corrections in stochastic inflation

Abstract

Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. We adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochastic Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The latetime probability distribution, P(φ), for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-N models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order H 4 at late times and so does not generate a dramatic gravitational back-reaction.

Renormalization in open quantum field theory. Part I. Scalar field theory

“…1 Second, open relativistic QFTs are very relevant by themselves in heavy ion physics [19][20][21][22] and cosmology [23][24][25][26][27][28][29][30]. Third motivation is to better understand the apparently non-unitary evolution engendered by black holes and to give a quantitative characterization of the information loss.…”

Loop Corrections to Standard Model fields in inflation

“…This result can be found by simple estimation using Hartree-Fock approximation, or more rigorous stochastic approach [21][22][23][24][25][26], or through 1-loop resummation using dynamical renormalization group method [27,28] (see also [29][30][31][32] for related diagrammatic calculations). On the other hand, in the Euclidean version of dS, it was recognized that the 1-loop late-time divergence is from the improper treatment of scalar zero mode.…”

The quantum Fokker-Planck equation of stochastic inflation

“…Because of these subtleties, it is important to have a complete derivation of the stochastic description from the full quantum theory using many different approaches. 2 One recent approach [25,26] to this problem has been to consider the quantum evolution of the theory from a different perspective by working in the Schrödinger picture. 3 In this picture, the connection between the classical probability function of the stochastic description and the quantum density matrix of the scalar theory becomes much clearer.…”

“…The essential element that was missing from these works was the fully quantum treatment of the interactions. In [25,26], the role of the interactions was only introduced as a background effect on an otherwise quadratic -purely Gaussian -theory.…”

“…We have now arrived at the quantum version of the Fokker-Planck equation, evaluated to linear order in the coupling, 26) where the quantum -momentum dependent -noise term is…”