Reconsidering holographic dark energy in Brans–Dicke theory

Abstract

In this paper, we reconsider the concept of holographic dark energy in the framework of Brans–Dicke theory in the formalism of the flat Friedmann–Lemaitre–Robertson–Walker metric. Firstly, we demonstrate how the assumption $$\phi \propto a^n$$ ϕ ∝ a n , where $$\phi $$ ϕ and a stand for the Brans–Dicke scalar field and scale factor, respectively, naturally leads to a constant deceleration parameter, irrespective of the energy content of the universe. Secondly, we consider interacting holographic dark energy with Hubble horizon as IR cut-off, and find the value of the Hubble parameter and corresponding value of the scale factor. Further, we find the value of the Brans–Dicke scalar field $$\phi $$ ϕ for the obtained value of the Hubble parameter and holographic dark energy. We obtain the corresponding value of the deceleration parameter and show that it can explain the phase transition of the universe. Moreover, statefinder diagnostics has been applied to compare the model with existing models. On the other hand, we consider the viscous behavior of holographic dark energy and show that the viscous holographic dark energy can play the role of interacting holographic dark energy as it is able to explain the phase transition of the universe. Further, we find the value of the Brans–Dicke scalar field $$\phi $$ ϕ for this viscous holographic dark energy. In this model also, we apply the statefinder diagnostic.