Geodesic deviation equation in Brans–Dicke theory in arbitrary dimensions

Abstract

In this paper, we study the geodesic deviation equation (GDE) within the context of the Brans-Dicke (BD) theory in $D$ dimensions. Then, we restrict our attention to the GDE for the fundamental observers and null vector field past directed. Concerning the latter, in order to apply the retrieved GDE for the cosmological models as well as examining exact solutions, we study some cosmological models in general relativity (GR) and in the context of the BD theory. For the BD framework, we provide two appropriate settings for dynamical system, which can be considered as the most extended case scenarios with respect to those studied previously. Then, we investigate a few well-known BD cosmological models, for which we present the modified and corrected exact solutions. Moreover, we show that the retrieved formalism of the GDE can also be properly applicable for the modified BD theory (MBDT), whose matter and potential emerge from the geometry. For all of our herein cosmological models, we investigate the energy conditions and depict the behavior of the deviation vector and observer area distance. We demonstrate that why the MBDT can be considered as a more appropriate candidate to describe the universe in accordance with the observational data as well as from theoretical viewpoint.