Exact cosmological solutions in modified Brans–Dicke theory

Abstract

In this paper, we obtain exact cosmological vacuum solutions for an extended FLRW homogeneous and isotropic Brans–Dicke (BD) universe in five dimensions for all values of the curvature index. Then, by employing the equations associated with a modified Brans–Dicke theory (MBDT) [], we construct the physics on a four-dimensional hypersurface. We show that the induced matter obeys the equation of state of a fluid of barotropic type. We discuss the properties of such induced matter for some values of the equation of state parameter and analyze in detail their corresponding solutions. To illustrate the cosmological behaviors of the solutions, we contrast our solutions with those of the standard BD theory. We find that, in the MBDT scenario, it is impossible to find a physically acceptable solution associated with the negative curvature for both the dust-dominated and radiation-dominated universes. However, for spatially flat and closed universes, we argue that our obtained solutions are more general than those associated with the standard BD theory and, moreover, they contain a few classes of solutions which have no analog in the BD cosmology. For these particular cases, we further compare the results with those extracted in the context of the induced-matter theory (IMT) and general relativity (GR). Furthermore, we discuss in detail the time behaviors of the cosmological quantities and compare them with recent observational data. We find a favorable range for the deceleration parameter associated with a matter-dominated spatially flat universe (for the late times), which is compatible with recent corresponding observational results.