Solid Consistency

TL;DR

This paper demonstrates that in solid inflation, isotropic long-wavelength scalar perturbations act as adiabatic modes after averaging over angles, even though ζ and 𝓡 evolve and do not coincide on super-horizon scales. By carefully exploiting gauge relations and computing cubic Lagrangians to O(ε), the authors show that Maldacena-style squeezed-limit consistency relations hold after angular averaging for correlators involving long-wavelength scalars with short-scale scalars or tensors. They verify these angle-averaged CRs for ⟨ζζζ⟩ and ⟨ζγγ⟩, including slow-roll corrections, and explain why 𝓡-based CRs become gauge- and model-dependent, though reheating restores ζ = 𝓡. The results imply that, within solid inflation’s symmetry structure, local non-Gaussianity cannot be generated through angle-averaged long-short couplings, with the short-mode scaling determining the fixed long-short correlations regardless of reheating dynamics.

Abstract

We argue that $isotropic$ scalar fluctuations in solid inflation are adiabatic in the super-horizon limit. During the solid phase this adiabatic mode has peculiar features: constant energy-density slices and comoving slices do not coincide, and their curvatures, parameterized respectively by $ζ$ and $\mathcal R$, both evolve in time. The existence of this adiabatic mode implies that Maldacena's squeezed limit consistency relation holds after angular average over the long mode. The correlation functions of a long-wavelength spherical scalar mode with several short scalar or tensor modes is fixed by the scaling behavior of the correlators of short modes, independently of the solid inflation action or dynamics of reheating.