Solid Soft Theorems

TL;DR

This work derives cosmological soft theorems for solids coupled to gravity by constructing the full set of solid adiabatic modes and exploiting their nonlinearly realized symmetries via the operator product expansion. It shows that Maldacena's consistency relation is recovered only after angular averaging over the long-mode direction and extends soft-theorem structure to soft tensor and vector perturbations, including mixed SVT sectors and higher-order $(q)$ terms in the trispectrum. The method hinges on a symmetry-based adiabatic-mode analysis in both uniform-density and uniform-density unitary gauges, valid on accelerated FLRW backgrounds with BD vacua, even in the presence of super-Hubble anisotropic stresses intrinsic to solids. The results provide model-independent relations among correlators, constrain the squeezed-limit coefficients, and offer concrete predictions for scalar, vector, and tensor soft limits with implications for CMB and LSS observables. Overall, the solid-inflation framework demonstrates how a nonstandard symmetry-breaking pattern imprints distinctive soft theorems on cosmological correlators, motivating further exploration of other symmetry-breaking scenarios and observational tests.

Abstract

We derive cosmological soft theorems for solids coupled to gravity. To this end, we first derive all cosmological adiabatic modes for solids, which display the interesting novelty of non-vanishing anisotropic stresses on large scales. Then, from the corresponding symmetries of the action of perturbations we compute the leading order related soft theorems using the operator product expansion. For the scalar bispectrum, we re-derive the result that Maldacena's consistency relation is recovered only upon angular averaging over the long mode direction. In addition, we find theorems for soft tensor and vector perturbations. In passing, we also clarify the derivation of these soft theorems in gauges where no residual diffeomorphisms exist.