Particle Seminar: Tim Cohen (U. Oregon) “Stochastic Inflation at NNLO”

Understanding the dynamics of light fields in a de Sitter (dS) spacetime is of both conceptual and phenomenological importance. To first approximation, a massless scalar field $\phi$ experiences quantum vacuum fluctuations sourced by the background geometry that manifest as Gaussian noise along with a restoring force due to the classical potential. The framework known as Stochastic Inflation incorporates these two effects to determine the probability distribution for the RMS value of $\phi$ by casting this problem in terms of a Focker-Planck equation, providing a leading approximation. In this talk, I will show how to extend this program to next-to-next-to leading order (NNLO) using Soft de Sitter Effective Theory to simplify and systematize the calculation, including a review of this new EFT framework. Then I will discuss how to start from the UV potential $\lambda \phi^4$, and perform the associated matching onto the EFT to one-loop order. This serves as the input to extract the NLO and NNLO corrections to Stochastic Inflation. A new feature emerges at NNLO, namely a universal correction that manifests as a higher derivative term in the Focker-Planck equation, which can be interpreted physically as a non-Gaussian contribution to the noise. I will discuss the implications of this new effect on the dynamics of light scalar fields in dS.