Testing Graviton Parity and Gaussianity with Planck T-, E- and B-mode Bispectra

Many inflationary theories predict a non-Gaussian spectrum of primordial tensor perturbations, sourced from non-standard vacuum fluctuations, modified general relativity or new particles such as gauge fields. Several such models also predict a chiral spectrum in which one polarization state dominates. In this work, we place constraints on the non-Gaussianity and parity properties of primordial gravitational waves utilizing the Planck PR4 temperature and polarization dataset. Using recently developed quasi-optimal bispectrum estimators, we compute binned parity-even and parity-odd bispectra for all combinations of CMB T-, E- and B-modes with $2\leq \ell<500$, and perform both blind tests, sensitive to arbitrary three-point functions, and targeted analyses of a well-motivated equilateral gravitational wave template (sourced by gauge fields), with amplitude $f_{\rm NL}^{ttt}$. This is the first time B-modes have been included in primordial non-Gaussianity analyses; they are found to strengthen constraints on the parity-even sector by $\simeq 30\%$ and dominate the parity-odd bounds, without inducing bias. We report no detection of non-Gaussianity (of either parity), with the template amplitude constrained to $f_{\rm NL}^{ttt}=900\pm 700$ (stable with respect to a number of analysis variations), compared to $1300\pm1200$ in Planck 2018. The methods applied herein can be reapplied to upcoming CMB datasets such as LiteBIRD, with the inclusion of B-modes poised to dramatically improve future bounds on tensor non-Gaussianity.