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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.14283 |
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| _version_ | 1866911596631031808 |
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| author | Beneke, Martin Hager, Patrick Sanfilippo, Andrea F. |
| author_facet | Beneke, Martin Hager, Patrick Sanfilippo, Andrea F. |
| contents | 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 $φ_+^2$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14283 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum correction to the diffusion term in stochastic inflation from composite-operator matching in Soft de Sitter Effective Theory Beneke, Martin Hager, Patrick Sanfilippo, Andrea F. High Energy Physics - Theory Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology 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 $φ_+^2$, 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. |
| title | Quantum correction to the diffusion term in stochastic inflation from composite-operator matching in Soft de Sitter Effective Theory |
| topic | High Energy Physics - Theory Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2604.14283 |