arXiv subjects

Andrea F. Sanfilippo

Publications and source records attributed to Andrea F. Sanfilippo.

4 recordsLinked to original sources

arXiv2026

Renormalisation and matching of massless scalar correlation functions in Soft de Sitter Effective Theory

For light and massless scalar fields, cosmological correlation functions suffer from infrared divergences and secular logarithms. Soft de Sitter Effective Theory (SdSET) has been proposed by Cohen and Green as the effective description of the non-trivial dynamics of long-wavelength modes $k_{\rm phys} < H$ in de Sitter space, which is responsible for the infrared and late-time logarithms, and as a systematic extension of the stochastic approach. In this article, we construct SdSET in dimensional regularisation, including an initial-condition functional. We demonstrate by examples that renormalisation and matching works as for flat-space effective field theories. Adopting massless $κϕ^4$ theory as the UV theory, we match the tree-level trispectrum and six-point function, and the one-loop power spectrum to SdSET, verifying explicitly that SdSET is the appropriate effective field theory for the quantum dynamics of superhorizon modes.

hep-th↗

arXiv2026

Classical conformal invariance and superhorizon dynamics in de Sitter

Soft de Sitter Effective Theory is a well-motivated candidate for the correct effective late-time description of equal-time correlation functions in de Sitter space. In this work, we study its application to theories that enjoy classical conformal invariance, using the conformally-coupled $ϕ^4$-theory as a toy model. While quantum effects generate non-trivial late-time dynamics in such models, we argue that it is not described by the standard construction of the effective theory as discussed thus far in the literature. We show that the tree-level matching of the trispectrum onto the effective theory does not fit into the expected power-counting scheme, and we contrast it with the matching of the tree-level bispectrum in the conformally-coupled $ϕ^3$-theory, where it works consistently. We then propose a prescription to identify the leading superhorizon degrees of freedom in such theories, which should serve as the starting point for the construction of their late-time effective description. The interpretation of logarithms of the form $\log(-kη)$ in this context is briefly discussed.

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arXiv2026

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

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.

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arXiv2023

Cosmological Correlators in massless $ϕ^4$-theory and the Method of Regions

The calculation of loop corrections to the correlation functions of quantum fields during inflation or in the de~Sitter background presents greater challenges than in flat space due to the more complicated form of the mode functions. While in flat space highly sophisticated approaches to Feynman integrals exist, similar tools still remain to be developed for cosmological correlators. However, usually only their late-time limit is of interest. We introduce the method-of-region expansion for cosmological correlators as a tool to extract the late-time limit, and illustrate it with several examples for the interacting, massless, minimally coupled scalar field in de~Sitter space. In particular, we consider the in-in correlator $\langleϕ^2(η,q)ϕ(η,k_1)ϕ(η,k_2)\rangle$, whose region structure is relevant to anomalous dimensions and matching coefficients in Soft de Sitter effective theory.

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