The electrodynamics with a Chern-Simons term
pĪ¼āAĪ½āFĪ¼Ī½ violates Lorentz and CPT symmetries
with a non-vanishing pĪ¼ā. For a fixed vector pĪ¼ā, 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.Comment: 11 pages, 1 figure, the version to appear in Physics Letters