Measuring chiral gravitational waves in Chern-Simons gravity with CMB bispectra

Chern-Simons gravity coupled to the scalar sector through a generic coupling function f(ϕ) can be tested at the very high energies of the inflationary period. In 1706.04627, we computed the theoretical parity breaking signatures of the ⟨γγζ⟩ primordial bispectrum which mixes two gravitons and one scalar curvature perturbation. We defined a parameter Π which measures the level of parity breaking of the corresponding bispectrum. In this work we forecast the expected 1σ error on Π using the cosmic microwave background (CMB) angular bispectra. We find that, given the angular resolution of an experiment like Planck, Π∼10^6 is detectable via the measurement of BBT or BBE angular bispectra if the tensor-to-scalar ratio r=0.01. We also show that, from the theoretical point of view, Π can be greater than 10^6. Thus, our conclusion is that BBT or BBE CMB angular bispectra can become an essential observable for testing Chern-Simons gravity in the primordial universe.