Primordial Stochastic Gravitational Wave Background Anisotropies: in-in Formalization and Applications

TL;DR

This paper develops a formalism using the in-in approach to calculate anisotropies in the primordial stochastic gravitational wave background caused by non-Gaussianities, applying it to various inflationary models and identifying potential detectable signals.

Contribution

It introduces the in-in formalism for explicitly deriving anisotropies in the gravitational wave background, extending analysis to multi-field models and loop corrections, and connects to observable signatures.

Findings

Derived explicit anisotropy expressions using in-in formalism.

Applied method to single-field and multi-field inflation models.

Identified potential for detectable gravitational wave anisotropies.

Abstract

Primordial non-Gaussianities of the scalar(tensor)-tensor-tensor type supporting a non-trivial squeezed component are known to induce anisotropies in the stochastic gravitational wave background. We derive the explicit form of such anisotropies by making use, for the first time in this context, of the in-in formalism for cosmological correlation functions. After illustrating the general method and using it for the minimal single-field slow-roll case, we apply it to multi-field models, providing both a tree-level and a one-loop example. First, we make contact with previous results on anisotropies due to the presence of an extra spin-2 field during inflation. Secondly, we calculate the 1-loop scalar-tensor-tensor three-point function in the context of so-called supersolid inflation. The corresponding gravitational wave anisotropy is induced atop a gravitational signal that may be sufficiently large for detection.