Consistently violating the non-Gaussian consistency relation

TL;DR

The paper investigates how single-field non-attractor inflation, notably ultra slow-roll, affects the Maldacena non-Gaussian consistency relation. Using symmetry arguments, it shows that the squeezed-limit of the bispectrum remains governed by background evolution, leading to a generalized relation that depends on the sound speed $c_s$ and the slow-roll parameter combination $\eta$. This general framework extends to broader non-attractor backgrounds including $P(X,\phi)$ theories, yielding a universal squeezed-limit form $\lim_{k_3\to 0} B_{\mathcal{R}} = \frac{3}{c_s^2}(4+\eta)P_{\mathcal{R}}(k_1)P_{\mathcal{R}}(k_3)$ and clarifies how long-wavelength perturbations (e.g., $\mathcal{Q}$ or $\mathcal{F}$) can freeze despite evolving curvature perturbations. The findings reconcile the apparent violation in USR with a symmetry-based understanding and have important implications for interpreting non-Gaussianity measurements in current and upcoming cosmological surveys.

Abstract

Non-attractor models of inflation are characterized by the super-horizon evolution of curvature perturbations, introducing a violation of the non-Gaussian consistency relation between the bispectrum's squeezed limit and the power spectrum's spectral index. In this work we show that the bispectrum's squeezed limit of non-attractor models continues to respect a relation dictated by the evolution of the background. We show how to derive this relation using only symmetry arguments, without ever needing to solve the equations of motion for the perturbations.