Stochastic inflation from a non-equilibrium renormalization group

Abstract

Understanding stochastic inflation, and in particular the systematic computation of controlled corrections from first principles, remains an important open problem. In this work, we address this problem from two complementary perspectives. First, we derive the effective field theory governing long-wavelength modes from the reduced density matrix of a coarse-grained description. In this framework, locality in time follows from the thin-shell approximation, while locality in space is recovered dynamically in the super-Hubble regime. The resulting open effective field theory contains both dissipative and diffusive operators, with diffusion dominating as the coarse-graining scale is pushed into the infrared. This construction reproduces the usual Fokker-Planck equation at leading order and allows us to compute its corrections, including subleading contributions to the stochastic dynamics. Second, we study the evolution of the density matrix under changes of the coarse-graining scale. We show that this flow is governed by a Polchinski-type renormalisation group equation formulated directly for the density matrix. Dissipative and diffusive operators are generated dynamically along the flow, and the resulting effective action matches the Schwinger-Keldysh description. We derive a generalised Fokker-Planck equation directly from the renormalisation group flow, systematically incorporating subleading corrections and recovering the results obtained in the open effective field theory approach.