Primordial stochastic gravitational wave background anisotropies: in-in formalization and applications

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.

Automated summary

For the first time, this study derives the explicit form of the anisotropies induced by the scalar(tensor)-tensor-tensor type of primordial non-Gaussianities in the stochastic gravitational wave background using the in-in formalism. The method is applied to both single-field slow-roll and multi-field models, providing examples at tree-level and one-loop. The results are compared to previous findings on anisotropies during inflation and offer the potential for detection of the induced gravitational wave anisotropy atop a gravitational signal.