Stochastic Inflation at NNLO
Timothy Cohen, Daniel Green, Akhil Premkumar, and Alexander Ridgway

TL;DR
This paper advances the theoretical understanding of Stochastic Inflation by calculating NNLO corrections using SdSET, revealing the role of non-Gaussian fluctuations and confirming the formalism's consistency beyond tree level.
Contribution
It provides the first NNLO correction to Stochastic Inflation, derived from two-loop anomalous dimensions, and demonstrates the systematic incorporation of higher order effects within SdSET.
Findings
NNLO corrections significantly impact the equilibrium distribution.
Matching UV theory onto SdSET confirms the persistence of Wilson-coefficient corrections.
Logarithmic divergences affect the factorization in SdSET, leading to renormalization group flow.
Abstract
Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO,…
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