Introduction of the generalized Lorenz gauge condition into the vector-tensor theory

TL;DR

This paper introduces a generalized Lorenz gauge condition into vector-tensor gravity theories, analyzing its effects on cosmic evolution and static solutions, revealing potential roles as cosmological constant or dark matter.

Contribution

It is the first to incorporate the generalized Lorenz gauge into vector-tensor gravity theories and study its implications for cosmology and static solutions.

Findings

Vector field behaves as cosmological constant when minimally coupled.

Vector field can act as dark matter when nonminimally coupled.

Energy conditions and stability constrain model parameters.

Abstract

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.