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Many inflationary theories predict a non-Gaussian spectrum of primordialtensor perturbations, sourced from non-standard vacuum fluctuations, modifiedgeneral relativity or new particles such as gauge fields. Several such modelsalso predict a chiral spectrum in which one polarization state dominates. Inthis work, we place constraints on the non-Gaussianity and parity properties ofprimordial gravitational waves utilizing the Planck PR4 temperature andpolarization dataset. Using recently developed quasi-optimal bispectrumestimators, we compute binned parity-even and parity-odd bispectra for allcombinations of CMB T-, E- and B-modes with $2\leq \ell<500$, and perform bothblind tests, sensitive to arbitrary three-point functions, and targetedanalyses of a well-motivated equilateral gravitational wave template (sourcedby gauge fields), with amplitude $f_{\rm NL}^{ttt}$. This is the first timeB-modes have been included in primordial non-Gaussianity analyses; they arefound to strengthen constraints on the parity-even sector by $\simeq 30\%$ anddominate the parity-odd bounds, without inducing bias. We report no detectionof non-Gaussianity (of either parity), with the template amplitude constrainedto $f_{\rm NL}^{ttt}=900\pm 700$ (stable with respect to a number of analysisvariations), compared to $1300\pm1200$ in Planck 2018. The methods appliedherein can be reapplied to upcoming CMB datasets such as LiteBIRD, with theinclusion of B-modes poised to dramatically improve future bounds on tensornon-Gaussianity.

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