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

Abstract

Chern-Simons gravity coupled to the scalar sector through a generic coupling function $f(\ddot{I}•)$ can be tested at the very high energies of the inflationary period. In 1706.04627, we computed the theoretical parity breaking signatures of the $⟨{\hat{I}}^3{\hat{I}}^3\hat{I}\P ⟩$ primordial bispectrum which mixes two gravitons and one scalar curvature perturbation. We defined a parameter $\hat{I}$ which measures the level of parity breaking of the corresponding bispectrum. In this work we forecast the expected $1\ddot{I}ƒ$ error on $\hat{I}$ using the cosmic microwave background (CMB) angular bispectra. We find that, given the angular resolution of an experiment like $Planck$, $\hat{I}\sim 10^6$ 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, $\hat{I}$ 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.

16 pages, 1 figure; version matching publication in JCAP