  We derive, in curved spacetime, the most general Lorentz-violating
electromagnetic Lagrangian containing dimension-five operators with one more
derivative than the Maxwell term in the hypothesis that Lorentz symmetry is
broken by a background four-vector $n_\mu$. We then study, for the case of
isotropic $n_\mu$, the generation of cosmic magnetic fields at inflation and
cosmic birefringence. In the limiting case of Minkowski spacetime, we find that
other than the CPT-odd Myers-Pospelov term, there exists another CPT-odd term
that gives rise to nontrivial dispersion and constitutive relations.
