Tensor Squeezed Limits and the Higuchi Bound

TL;DR

Tensor consistency relations are more universal than scalar ones during inflation, guaranteed by the Higuchi bound, and their potential violation could signal models like solid inflation with anisotropic features.

Contribution

This paper demonstrates the universality of tensor consistency relations beyond scalar cases and links their validity to the Higuchi bound during inflation.

Findings

Tensor consistency relations hold in multi-field inflation with fast anisotropy decay.

The Higuchi bound ensures the absence of light higher-spin particles, supporting these relations.

Potential observational signatures include graviton exchange effects and quadrupolar anisotropies.

Abstract

We point out that tensor consistency relations-i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum-are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: De Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor con- sistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) Graviton exchange contribution to the scalar four-point function; (b) Quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.