Probing parity-odd bispectra with anisotropies of GW $V$ modes

It is well known that non-trivial squeezed tensor bispectra can lead to anisotropies in the inflationary stochastic gravitational wave (GW) background, providing us with an alternative and complementary window to primordial non-Gaussianities (NGs) with respect to the CMB. Previous works have highlighted the detection prospects of parity-even tensor NGs via the GW $I$-mode anisotropies. In this work we extend this by analysing for the first time the additional information carried by GW $V$-mode anisotropies due to squeezed NGs. We show that GW $V$ modes allow us to probe parity-odd squeezed $\langle \rm tts \rangle$ and $\langle \rm ttt \rangle$ bispectra. These bispectra break parity at the non-linear level and can be introduced by allowing alternative symmetry breaking patterns during inflation, like those comprised in solid inflation. Considering a BBO-like experiment, we find that a non-zero detection of squeezed $\langle \rm tts \rangle$ parity-odd bispectra in the $V$ modes dipole is possible without requiring any short-scale enhancement of the GW power spectrum amplitude over the constraints set by the CMB. We also briefly discuss the role of $V$-CMB cross-correlations. Our work can be extended in several directions and motivates a systematic search for polarized GW anisotropies in the next generations of GW experiments.