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arXiv · 2601.22644

Nonlocal Corrections to Scalar Field Effective Action in de Sitter spacetime

Will Cerne·Teruaki Suyama
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Abstract

We investigate the one-loop effective action for a test scalar field in a general Friedmann-Lema\^itre-Robertson-Walker (FLRW) background, specifically focusing on quantum corrections up to the second order in the interaction strength. By employing the Schwinger-Keldysh formalism, we derive the equation of motion for the field expectation value, which incorporates not only the standard local radiative corrections but also novel nonlocal features: a memory term and a stochastic noise term. We identify all ultraviolet divergent structures within these nonlocal terms and provide a consistent renormalization procedure. To analyze the physical impact of these terms, we apply a local approximation under the assumption of slowly-varying fields, by which the memory term acts as a negative contribution to the drift coefficient. As a concrete application, we consider a massive $\phi^4$ theory and show that these one-loop corrections lead to a suppression of the field variance in the infrared regime compared to the tree-level results.

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Will Cerne, Teruaki Suyama. 2026-01-30. Nonlocal Corrections to Scalar Field Effective Action in de Sitter spacetime. https://arxiv.org/abs/2601.22644

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