Soft Theorems For Shift-Symmetric Cosmologies

TL;DR

This work develops shift-symmetric adiabatic modes (SAMs) for single-clock cosmologies with a shift symmetry, extending Weinberg's adiabatic modes by combining a large diffeomorphism with an internal shift. Using SAMs and an operator product expansion, the authors derive general soft theorems for $n$-point correlators in the squeezed limit, fixing leading OPE coefficients via dilation and shift symmetries. They validate the framework by reproducing the squeezed bispectrum for Ultra-Slow-Roll inflation, where the background is non-attractor and $\zeta$ does not freeze on superhorizon scales, yielding $\langle \zeta_q \zeta_k \zeta_{-k} \rangle' \to 6P(k)P(q)$ and $f_{NL}=5/2$. The results illuminate the infrared structure of shift-symmetric cosmologies and highlight model-dependent corrections away from attractor behavior, informing how soft theorems constrain non-attractor dynamics.

Abstract

We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift-symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for Ultra-slow-roll inflation, a particular shift-symmetric, non-attractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.