$\lambda\phi^4$ as an Effective Theory in de Sitter

TL;DR

This paper analyzes effective field theories for scalar fields in de Sitter space, revealing how the cutoff scale influences unitarity, state evolution, and the sign of the quartic coupling, with implications for cosmological models.

Contribution

It provides a complete analytic matching of $bbb4$ theories with UV models, highlighting non-unitary effects and the behavior of the quartic coupling as the cutoff varies.

Findings

Unitary description when cutoff is above horizon scale

Emergence of mixed states and diffusive effects below horizon scale

Loop-level matching shows quartic coupling becomes negative as cutoff decreases

Abstract

Effective field theories (EFTs) provide a powerful framework to parametrise unknown aspects of possible ultraviolet (UV) physics. For scalar fields in de Sitter space, however, new emergent phenomena can arise when the cut-off scale of the theory lies below the horizon scale $H$, as seen in the stochastic formalism of inflation. In this work, we study EFTs that, at leading order, reproduce the standard quartic theory in de Sitter, but with a variable cut-off identified with the mass of an integrated-out hidden sector. We perform the complete analytic computation for the tree- and loop-level matching between the effective $\lambda\phi^4$ theory and two possible UV realisations. We find that when the cut-off is much larger than the horizon, the theory admits a unitary description, up to exponentially suppressed corrections. In contrast, when the cut-off is lowered below $H$, the system evolves into a mixed state and diffusive effects emerge. Nevertheless, at leading order, the EFT remains local and reproduces the same effective quartic coefficient as in the unitary regime. Furthermore, for the EFT matching at the loop-level, the effective quartic coupling changes sign and becomes negative as the cut-off decreases, in agreement with the result obtained from the stochastic formalism. In general, for cosmological EFTs, our findings highlight the role of non-unitary effects and illustrate their regimes of validity, within and beyond perturbation theory.