Chern-Simons gravitational term coupled to an isocurvature field

Abstract: The Chern-Simons gravitational term is typically coupled to the inflaton field during inflation. However, this setup leads to ghost instabilities in the tensor sector, which severely constrain observable signatures of parity violation in cosmological correlators. In this work, we explore an alternative scenario where the Chern-Simons term is minimally coupled to an isocurvature field, $\sigma$, within a multi-field inflationary framework. Notably, this configuration leaves the quadratic action for tensor perturbations unaffected, thereby avoiding ghost instabilities. We analyze the resulting phenomenology and show that the model allows for parity-violating signatures and distinctive features in the primordial scalar-tensor bispectra, while remaining theoretically consistent and observationally viable.