A simple parity violating gravity model without ghost instability

Abstract

In this paper we consider a parity violating gravity model without higher derivatives, thus ghost free. This model is constructed from the tetrad and its derivatives and coupled to a dynamical scalar field, like axion. It can be reduced from the Nieh-Yan term within the framework of teleparallel gravity. We apply this model to cosmology and investigate its consequences on cosmological perturbation theory. We find that the coupled dynamical scalar field lost its independent dynamics at the linear order and the parity violating term itself behaves like a viscosity. For gravitational waves, this model produces velocity difference between left- and right-handed polarizations, but generates no amplitude discrepancy.

Teleparallel axions and cosmology

“…We have proposed a new class of teleparallel gravity theories featuring a pseudo-scalar field with two independent couplings to the two pseudo-scalar torsion invariants, in order to obtain the most general class of teleparallel gravity theories which are parity-invariant and quadratic in the torsion tensor, without additional derivative terms. This model is a natural generalization of the model presented in [41,42], where only a single coupling to the Nieh-Yan term [43] is considered.…”

“…We finally remark that although the axion enters the cosmological background equations only for the axial tetrad A θ a μ , it contributes to perturbations around all cosmological background tetrads, including the spatially flat tetrad obtained for k = 0 at the intersection of the axial and vector branches [41]. However, here we limit our discussion to the background dynamics of the homogeneous and isotropic FLRW spacetime, and leave the study of cosmological perturbations for future work.…”

“…Note that these are the only terms which contribute to the antisymmetric part of the field equations, since the remaining contributions from the kinetic and potential parts of the axion are symmetric tensors, and this holds also for the Einstein and energy-momentum tensors. Our axion and torsion modified general relativity is a straightforward generalization of the theory presented in [41,42], where the axion is coupled solely to the Nieh-Yan term (26). The latter is obtained from the model we just presented by fixing the parameters 2b + 9b = 0.…”

“…The parity-odd terms, however, have gained less attention in the literature so far. Recently they have been considered to construct a parity violating extension of TEGR [41,42], in which a pseudo-scalar field is coupled to the Nieh-Yan term [43].…”

“…In this article, we generalize the theory presented in [41,42] and construct the most general quadratic teleparallel theory of gravity employing all five quadratic torsion scalar terms. In particular, we use the two parity-odd torsion to naturally couple a pseudo-scalar field to gravity, which we call teleparallel axion.…”