Introduction of the generalized Lorentz 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 the spatially flat Friedmann-Robertson-Walker Universe. But it may not be 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.

Figure 1

The equation of state $w_A$ of the four-vector field $A^{\mu }$ with the ratio $r$ of $b_1$ and $b_2$. It is not bounded both below and up, namely, $-\infty <w_A<+\infty$.