  We consider the one-loop renormalization of QED in curved space-time with
additional Lorentz and/or CPT breaking terms. The renormalization group
equations in the vacuum sector are derived. In the special case of Minkowski
metric and with constant Lorentz and CPT breaking terms these equations reduce
to the ones obtained earlier by other authors. The necessary form of the vacuum
counterterms indicate possible violations of the space or time homogeneity or
space isotropy in the gravitational phenomena. However, the necessity of the
phenomenologically most interesting terms such as linear in the space-time
curvature or torsion, is related to the non-constant nature of the
dimensionless Lorentz and CPT breaking parameters.
