Holographic dark energy in Brans–Dicke theory

Abstract

In this paper, the holographic dark-energy model is considered in Brans–Dicke theory, where the holographic dark-energy density ρ _Λ =3c ² M ²_pl L ⁻² is replaced by ρ _h=3c ² Φ(t)L ⁻². Here $\varPhi (t)=\frac{1}{8\pi G}$ is the time-variable Newton constant. With this replacement, it is found that no accelerated expansion for the universe will be achieved when the Hubble horizon is taken to play the role of an IR cut-off. When the event horizon is adopted as the IR cut-off, accelerated expansion for the universe is obtained. In this case, the equation of state of holographic dark energy, w _h, takes the modified form $w_{\mathrm{h}}=-\frac{1}{3}(1+\alpha+\frac{2}{c}\sqrt{ \varOmega _{\mathrm{h}}})$ . In the limit α→0, the ‘standard’ holographic dark energy is recovered. In the holographic dark-energy dominated epoch, power-law and de Sitter time-space solutions are obtained.