Introduction of the generalized Lorenz gauge condition into the
  vector-tensor theory
  We introduce the generalized Lorentz gauge condition in the theory of quantum
electrodynamics into the general vector-tensor theories of gravity. Then we
explore the cosmic evolution and the static, spherically symmetric solution of
the four dimensional vector field with the generalized Lorenz gauge. We find
that, if the vector field is minimally coupled to the gravitation, it behaves
as the cosmological constant. On the other hand, if it is nonminimally coupled
to the gravitation, the vector field could behave as vast matters in the
background of spatially flat Friedmann-Robertson-Walker Universe. But it may be
not the case. The weak, strong and dominant energy conditions, the stability
analysis of classical and quantum aspects would put constraints on the
parameters and so the equation of state of matters would be greatly
constrained.
