Chern-Simons gravitational term coupled to a spectator field

Abstract

The Chern-Simons gravitational term is typically coupled to the inflaton field during inflation. In this work, we explore an alternative scenario where the Chern-Simons term is minimally coupled to a massive spectator field, $\ddot{I}ƒ$, within a multi-field inflationary framework where the spectator field is linearly coupled to the inflaton. We derive the corresponding parity-violating cubic interaction Lagrangian involving the curvature, spectator and tensor perturbations and compute how it affects primordial scalar-tensor bispectra. We find that these correlators yield distinctive parity-odd shapes. Perturbativity and consistency bounds are derived, constraining the couplings and the amplitude of the associated non-Gaussianities.

38 pages, 9 figures, v4: final changes: 1) The effect of the $\ddot{I}ƒ-\ddot{I}•$ coupling on $\ddot{I}{ƒ}_0$ was considered. The new $\dot{\ddot{I}}{ƒ}_0$ now introduces a tighter constraint on the strength of primordial non-Gaussianity. 2) Instead of "isocurvature field", the terminology "spectator field" was implemented. Matched published version in JCAP