A possible consistent model of parity violations in the symmetric
  teleparallel gravity
  Many parity violating gravity models suffer from the ghost instability
problem. In this paper we consider a symmetric teleparallel gravity model which
extends the general relativity equivalent model by several parity violating
interactions between the gravitational field and a scalar field. These
interactions exclude higher derivatives and are quadratic in the non-metricity
tensor. Through investigations on the linear cosmological perturbations, our
results show that in general this model suffers from the difficulty caused by
the existence of ghost mode in the vector perturbations. However, in cases
where a special condition is imposed on the coefficients of these parity
violating interactions, this model can be ghost free.
