Effects of the kinetic coupling of matter to curvature

Abstract

We discuss the effects on the kinetic properties of the scalar field which is coupled to the Einstein tensor. We first discuss a model of unification of dark matter and dark energy in the context of the Generalized Horndeski Theory. We show that if the scalar field represents dark matter then, because of its coupling to curvature, during the matter-dominated area it has a slow cosmological evolution acting like a pressureless fluid, and at later cosmological times it acts as dark matter. Then, the gravitational collapse of a time-dependent scalar field is studied in a theory with negative cosmological constant. It was found that it takes more time for a black hole to be formed as the coupling is increased. We also discuss a holographic model of building a holographic superconductor in the presence of the derivative coupling. We found that this coupling plays the role of an impurity parameter on the boundary theory. Breaking the translational invariance near the critical temperature two phases in the dual theory were found, a metal phase for positive coupling and an insulating phase if the coupling is negative.