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 Weitzenböck 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 Weitzenböck 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.
- Received 31 July 2021
- Accepted 18 September 2021
DOI:https://doi.org/10.1103/PhysRevD.104.084077
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