Scalar Gravity and Higgs Mechanism

The role of the auxiliary scalar field $\phi$ in Brans-Dicke theory is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with $\phi$; and almost all of the fundamental components of our universe can be unified into the dynamical equation for $\phi$. As a generalization of Brans-Dicke theory, we propose a new gravity theory with a complex scalar field $\phi$ which is coupled to the cosmological curvature scalar. Through such a coupling the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running mass scale is obtained in which the gauge symmetry breaks spontaneously