Discrete cosmological models in the Brans–Dicke theory of gravity

Abstract

We consider the problem of building inhomogeneous cosmological models in scalar-tensor theories of gravity. This starts by splitting the field equations of these theories into constraint and evolution equations, and then proceeds by identifying exact solutions to the constraints. We find exact, closed form expressions for geometries that correspond to the initial data for cosmological models containing regular arrays of point-like masses. These solutions extend similar methods that have recently been applied to Einstein’s equations, and provides sufficient initial conditions to perform numerical integration of the evolution equations. We use our new solutions to study the effects of inhomogeneity in cosmologies governed by scalar-tensor theories of gravity, including the spatial inhomogeneity allowed in Newton’s constant. Finally, we compare our solutions to their general relativistic counterparts, and investigate the effect of changing the coupling constant between the scalar and tensor degrees of freedom.