Soft de Sitter Effective Theory

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.

Manifestly causal in-in perturbation theory about the interacting vacuum

“…See Refs. [5][6][7] for alternative recent discussions. We wish to address here though, a technical detail missing from the demonstration of the equivalence of Eqs.…”

Markovian dynamics in de Sitter

“…In λφ 4 theory, the lowest decay exponent is O( √ λ), which is indeed a non-perturbative result. Several works, including [3,4,5,6,7,8,9,10,11,12,13,14,15,16], have explored various aspects of the problem over the years. Among them [11] has been particularly illuminating to the author and answers the Poincaré patch version of our main question.…”

Anisotropic separate universe and Weinberg's adiabatic mode

“…More recently, based on the power counting of , the evolution of the adiabatic curvature perturbation under the influence of loops was discussed in Ref. [134].…”