$CPT$ Violating Electrodynamics and Chern-Simons Modified Gravity

Details $CPT$ Violating Electrodynamics and Chern-Simons Modified Gravity $CPT$ Violating Electrodynamics and Chern-Simons Modified Gravity

2009-07-29

arxiv.org/abs/0907.5159v2

Phys.Lett.B680:118-124,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/j.physletb.2009.08.053

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.

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