Tensor non-Gaussianity in chiral scalar-tensor theories of gravity

Violation of parity symmetry in the gravitational sector, which manifests into unequal left and right circular polarization states primordial waves, represents a way to test high-energy modifications general relativity. In this paper we study inflation within recently proposed chiral scalar-tensor theories gravity, that extend Chern-Simons gravity by including parity-violating operators containing first second derivatives non-minimally coupled scalar (inflaton) field. Given degeneracy between different at level power spectrum statistics, make detailed analysis violation on tensor non-Gaussianity. We show, with an explicit computation, no new contributions arise graviton bispectra if couplings are constant pure de Sitter phase. On other hand, coupling functions time-dependent during inflation, acquire non-vanishing from parity-breaking even exact limit, maximal signal squeezed equilateral configurations. also comment consistency relation three-point function modes class models discuss prospects detecting signatures through Cosmic Microwave Background $B$-mode bispectra.