[Paper Review] Revisit on the healthy parity violating gravity model: local Lorentz covariance

Mingzhe Li, Haomin Rao+1 more|arXiv (Cornell University)|Apr 14, 2021

Black Holes and Theoretical Physics4 citations

TL;DR

This paper restores local Lorentz covariance in a previously proposed ghost-free parity-violating gravity model by abandoning the Weitzenb"ock condition on the spin connection, transforming it from a pure tetrad theory into a fully Lorentz-covariant framework. The model is extended to general Friedmann-Robertson-Walker cosmological backgrounds, confirming prior results and yielding new insights into parity violation in teleparallel gravity.

ABSTRACT

Recently, based on the theory of teleparallel gravity, a simple and ghost free parity violating gravity model was proposed in arXiv:2007.08038, where the Weitzenbock 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 Weitzenbock 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 arXiv:2007.08038 where only the spatially flat background was considered. Through the investigations of this paper, we confirm the results obtained in arXiv:2007.08038 and in addition get some new results.

Motivation & Objective

• To restore local Lorentz covariance in a previously proposed ghost-free parity-violating gravity model that explicitly broke Lorentz symmetry via the Weitzenb"ock condition.
• To reformulate the model beyond a pure tetrad theory by allowing a non-zero spin connection, ensuring full local Lorentz invariance.
• To generalize the model's cosmological applications from spatially flat to general Friedmann-Robertson-Walker backgrounds.
• To confirm earlier findings from arXiv:2007.08038 while deriving new results in a more general and covariant framework.

Proposed method

• Abandon the Weitzenb"ock condition on the spin connection to restore local Lorentz symmetry in the teleparallel gravity formulation.
• Construct the action using the tetrad and spin connection fields without imposing torsionless constraints, preserving full local Lorentz covariance.
• Apply the new model to a general Friedmann-Robertson-Walker spacetime, allowing for curvature and non-zero spatial sections.
• Derive the field equations in the new covariant framework and analyze their cosmological implications.
• Compare the new results with those from arXiv:2007.08038 to verify consistency and identify novel contributions.
• Use the formalism to study parity violation effects in cosmological dynamics beyond the flat-space limit.

Experimental results

Research questions

• RQ1 How can local Lorentz symmetry be restored in a previously proposed parity-violating gravity model that broke this symmetry via the Weitzenb"ock condition?
• RQ2 What are the cosmological consequences of the new, fully Lorentz-covariant formulation when applied to general Friedmann-Robertson-Walker backgrounds?
• RQ3 Does the extended model retain the ghost-free and simple structure of the original model while achieving full covariance?
• RQ4 What new physical insights emerge from the generalization to non-flat FRW spacetimes compared to the flat case?
• RQ5 How do the field equations and dynamics differ in the new covariant formulation compared to the original tetrad-only version?

Key findings

• The model successfully restores local Lorentz covariance by removing the Weitzenb"ock condition on the spin connection, resulting in a fully covariant formulation.
• The new model is no longer a pure tetrad theory, as the spin connection contributes dynamically to the field equations.
• The cosmological solutions in general Friedmann-Robertson-Walker backgrounds confirm the earlier results from arXiv:2007.08038.
• New results emerge from the generalization to non-flat FRW spacetimes, extending the applicability of the model beyond spatially flat cases.
• The parity-violating terms remain ghost-free and structurally simple, preserving the key features of the original model.
• The framework allows for a consistent study of parity violation in cosmological settings with curvature, offering new avenues for phenomenological exploration.