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

TL;DR

This paper investigates how parity-violating operators in chiral scalar-tensor theories of gravity influence primordial gravitational wave non-Gaussianity, revealing that time-dependent couplings induce detectable parity-breaking signals in tensor bispectra.

Contribution

It provides a detailed analysis of tensor non-Gaussianity in chiral scalar-tensor theories, showing how time-dependent couplings lead to observable parity-breaking effects in primordial gravitational waves.

Findings

Constant couplings do not alter graviton bispectra in de Sitter.

Time-dependent couplings produce non-zero parity-violating contributions.

Maximal signals occur in squeezed and equilateral configurations.

Abstract

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