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arXiv · 2604.14283

Quantum correction to the diffusion term in stochastic inflation from composite-operator matching in Soft de Sitter Effective Theory

Martin Beneke·Patrick Hager·Andrea F. Sanfilippo
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Abstract

In the framework of Soft de Sitter Effective Theory (SdSET), the Fokker-Planck equation for the late-time dynamics of the massless minimally coupled scalar field and its extension to the Kramers-Moyal equation are obtained from operator mixing of composite operators of the effective superhorizon field. We construct the formalism for composite-operator renormalisation, mixing and matching in dimensional regularisation, allowing for computations beyond the leading order. The general formalism is illustrated in free SdSET, which already features non-trivial structures including the well-known diffusion coefficient for stochastic inflation. As explicit examples in the interacting theory, we renormalise the one-loop bispectrum and the two-loop one-point function of the composite operator $\varphi_+^2$, and match them onto their full-theory counterparts. These results allow us to determine the next-to-leading order (two-loop) correction to the diffusion term of the Fokker-Planck equation of stochastic inflation for the first time.

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Martin Beneke, Patrick Hager, Andrea F. Sanfilippo. 2026-04-15. Quantum correction to the diffusion term in stochastic inflation from composite-operator matching in Soft de Sitter Effective Theory. https://arxiv.org/abs/2604.14283

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