The Suyama-Yamaguchi consistency relation in the presence of vector fields

TL;DR

This paper investigates how vector fields during inflation influence primordial non-Gaussianity, confirming that the isotropic components obey the Suyama-Yamaguchi relation, which could help interpret cosmic microwave background anisotropies.

Contribution

It provides a complete tree level calculation of non-Gaussianity parameters in models with vector fields, extending the Suyama-Yamaguchi relation to anisotropic inflation scenarios.

Findings

Isotropic non-Gaussianity parameters obey the Suyama-Yamaguchi relation.

Vector fields induce anisotropies in primordial fluctuations.

Respective Suyama-Yamaguchi-like relations are derived for different non-Gaussianity definitions.

Abstract

We consider inflationary models in which vector fields are responsible for part or eventually all of the primordial curvature perturbation \zeta. Such models are phenomenologically interesting since they naturally introduce anisotropies in the probability distribution function of the primordial fluctuations that can leave a measurable imprint in the cosmic microwave background. Assuming that non-Gaussianity is generated due to the superhorizon evolution, we use the \delta N formalism to do a complete tree level calculation of the non-Gaussianity parameters f_{NL} and \tau_{NL} in the presence of vector fields. We isolate the isotropic pieces of the non-Gaussianity parameters, which anyway have contributions from the vector fields, and show that they obey the Suyama-Yamaguchi consistency relation \tau^{iso}_{NL}>=(6/5f^{iso}_{NL})^2. Other ways of defining the non-Gaussianity parameters, which could be observationally relevant, are stated and the respective Suyama-Yamaguchi-like consistency relations are obtained.