A simple parity violating model in the symmetric teleparallel gravity and its cosmological perturbations

Parity violating models based on the symmetric teleparallel gravity have been considered in literature, but their applications cosmology and especially features cosmological perturbations not fully explored. In this paper we consider such a model which modifies general relativity merely through parity non-conserved coupling, ?(x)QQ˜, within framework of gravity. We study detail its applications, linear perturbation theory. Besides already known violation tensor perturbations, find that vector are promoted to be dynamical degrees freedom, left- right-handed modes propagate with different velocities. More importantly, one is found ghost at high momentum scales, will give rise vacuum instability quantum theory perturbations.