We consider a modified version of Brans-Dicke theory (MBDT) in four dimensions (4D) obtained by applying the induced matter method Wesson to 5D generalized theory. In model consists pure vacuum, with no self-interacting potential, except for scalar field. Following Wesson’s protocol, we group geometric terms Einstein tensor arising from extra dimension, move them other side field equations, and...

Abstract In this paper, we reconsider the concept of holographic dark energy in framework Brans–Dicke theory formalism flat Friedmann–Lemaitre–Robertson–Walker metric. Firstly, demonstrate how assumption $$\phi \propto a^n$$ ϕ ∝ a n </mm...