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