Exact Cosmological Solutions in Modified Brans-Dicke Theory

TL;DR

This paper derives exact vacuum solutions in a five-dimensional modified Brans-Dicke cosmology, analyzes the induced four-dimensional matter, and compares the solutions with standard Brans-Dicke, induced matter theory, and observational data.

Contribution

It presents new exact solutions in modified Brans-Dicke theory that extend and generalize previous cosmological models, especially for flat and closed universes.

Findings

Solutions are more general than standard BD for flat and closed universes.

Negative curvature solutions are not physically acceptable in MBDT.

The deceleration parameter aligns with recent observational data for matter-dominated flat universe.

Abstract

In this paper, we obtain exact cosmological vacuum solutions for an extended FLRW homogenous and isotropic Brans-Dicke (BD) universe in five dimensions for all values of the curvature index. Then, by employing the equations associated to a modified Brans-Dicke theory (MBDT) [1], we construct the physics on a four-dimensional hypersurface. We show that the induced matter obeys the equation of state of a fluid of a barotropic type. We discuss the properties of such an 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 present the standard Brans-Dicke theory. We retrieve that, in MBDT scenario, it is impossible to find a physically acceptable solution associated to the negative curvature for both the dust-dominated and radiation-dominated universes. However, for a spatially flat and closed universes, we argue that our obtained solutions are more general than those associated to the standard BD theory and, moreover, they contain a few classes of solutions which have no analog in the BD cosmology. For those 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 to a matter-dominated spatially flat universe (for the late times) which is compatible with recent corresponding observational results.