EFTs for light fields in de Sitter and the emergence of the stochastic regime

Abstract: Effective field theories (EFTs) provide a systematic framework to parametrise unknown ultraviolet (UV) physics. In de Sitter space, the long-wavelength dynamics of light scalar fields is naturally described by stochastic inflation, which can be viewed as an EFT obtained after integrating out subhorizon modes. This framework highlights that qualitatively new behaviour arises when the EFT cutoff lies below the Hubble scale H. In this talk, we investigate two complementary ways of constructing and understanding EFTs in this regime.
First, we derive an EFT by integrating out heavy fields in a UV-complete theory, obtaining an effective lambdaphi^4description in de Sitter space with a cutoff set by the heavy mass scale. We perform a complete analytic matching to two explicit UV completions, including both tree-level and loop contributions. When the cutoff lies well above H, the EFT admits a unitary description, with exponentially suppressed corrections. When the cutoff is lowered below H, the effective dynamics becomes intrinsically non-unitary: the system evolves into a mixed state and exhibits diffusive behaviour, in close analogy with stochastic inflation.
Second, we construct an EFT directly by integrating out high-energy modes using a time-dependent cutoff, without reference to a specific UV completion. We show that the resulting effective dynamics reproduces the same physical predictions as the UV-matched theory. Together, these results provide a unified picture of EFTs for light fields in de Sitter space, interpolating between unitary and stochastic descriptions.