Ghost instability in the teleparallel gravity model with parity violations

In this paper we consider the parity violating gravity model within the framework of teleparallel gravity. The parity violations are caused by the couplings of a scalar field to the scalar invariants which are parity-odd and quadratic in the torsion tensor. Totally there are two such type independent invariants, and one of them is the Nieh-Yan density. Through investigations on the cosmological perturbations of this model, we find that in general it suffers from the difficulties of ghost instability in the scalar and vector perturbations. But in the special case only the coupling to the Nieh-Yan density exists, this model is ghost free and reduces to the Nieh-Yan modified Teleparallel Gravity model. We also analyze the severity of the ghost instability by studying the perturbations around the Minkowski background.