Soft de Sitter Effective Theory

TL;DR

We develop the Soft de Sitter Effective Theory (SdSET), an infrared EFT for superhorizon modes in de Sitter space that isolates growing and decaying solutions and organizes operators by a clear power counting in $\lambda = k/(aH)$. By integrating out short-distance modes and employing dynamical dimensional regularization, SdSET converts IR problems into UV matching and enables DRG-based resummation of logarithms, clarifying perturbation theory outside the horizon. For massive fields, horizon-exterior physics is irrelevant at leading order, while very light fields give marginal interactions that reproduce stochastic inflation through DRG flow. Extending to dynamical gravity, SdSET proves all-orders conservation of adiabatic density fluctuations and gravitational waves, and provides a controlled framework to study slow-roll eternal inflation and gravitational backreaction within a consistent EFT.

Abstract

Calculating the quantum evolution of a de Sitter universe on superhorizon scales is notoriously difficult. To address this challenge, we introduce the Soft de Sitter Effective Theory (SdSET). This framework holds for superhorizon modes whose comoving momentum is far below the UV scale, which is set by the inverse comoving horizon. The SdSET is formulated using the same approach that yields the Heavy Quark Effective Theory. The degrees of freedom that capture the long wavelength dynamics are identified with the growing and decaying solutions to the equations of motion. The operator expansion is organized using a power counting scheme, and loops can be regulated while respecting the low energy symmetries. For massive quantum fields in a fixed de Sitter background, power counting implies that all interactions beyond the horizon are irrelevant. Alternatively, if the fields are very light, the leading interactions are at most marginal, and resumming the associated logarithms using (dynamical) renormalization group techniques yields the evolution equation for canonical stochastic inflation. The SdSET is also applicable to models where gravity is dynamical, including inflation. In this case, diffeomorphism invariance ensures that all interactions are irrelevant, trivially implying the all-orders conservation of adiabatic density fluctuations and gravitational waves. We briefly touch on the application to slow-roll eternal inflation by identifying novel relevant operators. This work serves to demystify many aspects of perturbation theory outside the horizon, and has a variety of applications to problems of cosmological interest.