Holographic dark energy in the DGP braneworld with GO cutoff

TL;DR

This paper explores a holographic dark energy model within the DGP braneworld framework using the GO IR cutoff, deriving analytical expressions for key cosmological parameters and analyzing stability, which aligns with observations and offers a stable dark energy scenario.

Contribution

It provides the first analytical derivation of the evolution of the equation of state and deceleration parameters in this model, and demonstrates conditions for stability and a transition to accelerated expansion.

Findings

The model can transition from deceleration to acceleration around redshift 0.6.

Analytical expressions for w(z) and q(z) are derived.

The model can be stable with appropriate parameter choices.

Abstract

We consider the holographic dark energy (HDE) model in the framework of DGP braneworld with Granda-Oliveros infrared (IR) cutoff, $L=(\alpha \dot{H}+\beta H^2)^{-1/2}$. With this choice for IR cutoff, we are able to derive evolution of the cosmological parameters such as the equation of state and the deceleration parameters, $w$ and $q$, as the functions of the redshift parameter $z$. As far as we know, most previous models of HDE presented in the literatures, do not gives analytically $\omega=\omega(z)$ and $q=q(z)$. We plot the evolution of these parameters versus $z$ and discuss that the results are compatible with the recent observations. With suitably choosing the parameters, this model can exhibit a transition from deceleration to the acceleration around $z\approx 0.6$. Then, we suggest a correspondence between the quintessence and tachyon scalar fields and HDE in the framework of DGP braneworld. This correspondence allows us to reconstruct the evolution of the scalar fields and the scalar potentials. We also investigate stability of the presented model by calculating the squared sound speed, $v^2_s$, whose sign determines the stability of the model. Our study shows that $v^2_s$ could be positive provided the parameters of the model are chosen suitably. In particular, for $\alpha>1$, $\beta>0$, and $\alpha<1$, $\beta<0$, we have $v^2_s>0$ during the history of the universe, and so the stable dark energy dominated universe can be achieved. This is in contrast to the HDE in standard cosmology, which is unstable against background perturbations and so cannot lead to a stable dark energy dominated universe.