Revisiting a parity violating gravity model without ghost instability: Local Lorentz covariance

TL;DR

This paper revisits a parity violating gravity model based on teleparallel gravity, restoring local Lorentz symmetry and extending its application to general FRW backgrounds, confirming previous results and deriving new insights.

Contribution

It restores local Lorentz symmetry in a ghost-free parity violating gravity model and applies it to general FRW backgrounds, broadening previous flat-space studies.

Findings

Confirmed previous results on the model's properties.

Extended the model to general FRW backgrounds.

Derived new results related to cosmological applications.

Abstract

Recently, based on the theory of teleparallel gravity, a simple and ghost free parity violating gravity model was proposed in [M. Li, H. Rao, and D. Zhao, J. Cosmol. Astropart. Phys. 11 (2020) 023], where the Weitzenb\"{o}ck connection was adopted for simplifying the calculations but breaks the local Lorentz symmetry explicitly. In this paper, we restore the local Lorentz symmetry of this model by giving up the Weitzenb\"{o}ck condition on the spin connection. With full local Lorentz covariance, this model is not a pure tetrad theory any more. We also apply the new version of this model to the universe with general Friedmann-Robertson-Walker background. This further generalizes the studies of [M. Li, H. Rao, and D. Zhao, J. Cosmol. Astropart. Phys. 11 (2020) 023] where only the spatially flat background was considered. Through the investigations of this paper, we confirm the results obtained in [M. Li, H. Rao, and D. Zhao, J. Cosmol. Astropart. Phys. 11 (2020) 023] and in addition get some new results.