Holographic Dark Energy in Brans-Dicke Theory

TL;DR

This paper explores holographic dark energy within Brans-Dicke theory, showing that accelerated expansion depends on the choice of IR cutoff, and derives modified equations of state and specific cosmological solutions.

Contribution

It introduces a modified holographic dark energy model in Brans-Dicke theory with a time-varying Newton constant, analyzing conditions for accelerated expansion and deriving new solutions.

Findings

Accelerated expansion occurs only with the event horizon as IR cutoff.

Modified equation of state for holographic dark energy is derived.

Power-law and de Sitter solutions are obtained in the dark energy dominated epoch.

Abstract

In this paper, the holographic dark energy model is considered in Brans-Dicke theory where the holographic dark energy density $\rho_{\Lambda} =3c^2 M^{2}_{pl} L^{-2}$ is replaced with $\rho_{h}=3c^2 \Phi(t)L^{-2}$. Here $\Phi(t)=\frac{1}{8\pi G}$ is a time variable Newton constant. With this replacement, it is found that no accelerated expansion universe will be achieved when the Hubble horizon is taken as the role of IR cut-off. When the event horizon is adopted as the IR cut-off, an accelerated expansion universe is obtained. In this case, the equation of state of holographic dark energy $w_h$ takes a modified form $w_h=-{1/3}(1+\alpha+\frac{2}{c}\sqrt{\Omega_{h}})$. In the limit $\alpha\to 0$, the 'standard' holographic dark energy is recovered. In the holographic dark energy dominated epoch, power-law and de Sitter time-space solutions are obtained.