$CPT$ Violating Electrodynamics and Chern-Simons Modified Gravity

Abstract

The electrodynamics with a Chern-Simons term $p_{\mu }{A}_{\nu }{\tilde{F}}^{\mu \nu }$ 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.

11 pages, 1 figure, the version to appear in Physics Letters B

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