  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.
