Stochastic inflation with interacting noises

Abstract Stochastic δ N formalism is a powerful tool to calculate the cosmological correlators non-perturbatively. However, it requires the initial data for the amplitude of the noise on the initial flat hypersurface which for a free theory during inflation is fixed to be H /2π. In this work, we study the setups where the underlying theory involves interactions and the stochastic noises inherit these interactions. We extend the stochastic δ N formalism to these setups and rewrite the corresponding Langevin and Fokker-Planck equations in which the QFT corrections in the amplitude of the noises are taken into account. As an example, in the three-phase SR-USR-SR setup which is employed for PBHs formation, the modification in the amplitude of noise is calculated from the one-loop corrections in power spectrum via in-in formalism. We show that in these setups the amplitude of the stochastic noise is modified to H /2π(1+ Δ𝒫 ℛ /𝒫 (0) ℛ ) 1/2 in which Δ𝒫 ℛ /𝒫 (0) ℛ is the fractional one-loop correction in power spectrum.