$CPT$ Violating Electrodynamics and Chern-Simons Modified Gravity

TL;DR

This paper investigates the inconsistencies in Chern-Simons modified electrodynamics coupled to gravity and proposes a consistent model by adding a Chern-Simons term to gravity, analyzing its effects on cosmic microwave background and gravitational waves.

Contribution

It introduces a consistent framework for Chern-Simons modified gravity coupled with electrodynamics, addressing divergence issues and exploring cosmological phenomenologies.

Findings

Symmetric but non-divergence-free energy-momentum tensor in the original model

Modified gravity sector with Chern-Simons term ensures consistency

Potential observable effects on cosmic microwave background and gravitational waves

Abstract

The electrodynamics with a Chern-Simons term $p_{\mu}A_{\nu}\widetilde{F}^{\mu\nu}$ violates Lorentz and $CPT$ symmetries with a non-vanishing $p_{\mu}$. For a fixed vector $p_{\mu}$, in this paper we point out that the energy-momentum tensor of this theory coupled to the gravity minimally is symmetric but not divergence free, which consequently makes the gravitational field equation inconsistent. To preserve the consistency, we introduce a Chern-Simons term in the gravity sector with the coefficient determined by the Lorentz and $CPT$ violating term in the electromagnetic field. Further we study the phenomenologies of the model on the cosmic microwave background radiation and the relic gravitational waves.