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

TL;DR

This paper investigates the potential of CMB bispectra to detect parity-breaking signatures from Chern-Simons gravity during inflation, proposing that specific angular bispectra could serve as key observables for testing this theory.

Contribution

It forecasts the detectability of parity-breaking signatures in CMB bispectra, linking theoretical predictions with observational prospects for Chern-Simons gravity.

Findings

Detectable parity-breaking parameter $$ can be as high as 10^6.

CMB $BBT$ and $BBE$ bispectra are promising observables.

Experiments like Planck could detect $$ around 10^6 with $r=0.01$.

Abstract

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