Cosmological Perturbations of Extended NGR Model with Parity Violation

Recently the modified teleparallel gravity models attracted a lot of interests. In this paper we consider more extensions to the New General Relativity (NGR) model with parity violations. This extended NGR model differs from the normal NGR model by the inclusion of additional parity-odd term that is quadratic in the torsion tensor. By investigating its cosmological perturbations of this model, we find that this model can avoid ghost instabilities in certain regions of the parameter space, where the coefficient of the parity-odd term does not vanish.