A simple parity violating gravity model without ghost instability

TL;DR

This paper introduces a ghost-free parity violating gravity model based on teleparallel gravity, coupling a scalar field to produce unique effects on cosmological perturbations and gravitational wave polarization.

Contribution

The paper presents a novel parity violating gravity model without higher derivatives, derived from the Nieh-Yan term, with implications for cosmology and gravitational wave polarization.

Findings

Scalar field loses independent dynamics at linear order

Parity violation acts like a viscosity in cosmology

Produces velocity difference between gravitational wave polarizations

Abstract

In this paper we consider a parity violating gravity model without higher derivatives, thus ghost free. This model is constructed from the tetrad and its derivatives and coupled to a dynamical scalar field, like axion. It can be reduced from the Nieh-Yan term within the framework of teleparallel gravity. We apply this model to cosmology and investigate its consequences on cosmological perturbation theory. We find that the coupled dynamical scalar field lost its independent dynamics at the linear order and the parity violating term itself behaves like a viscosity. For gravitational waves, this model produces velocity difference between left- and right-handed polarizations, but generates no amplitude discrepancy.