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Abstract
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We consider the holographic dark energy (HDE) model in the framework of the DGP braneworld with Granda-Oliveros infrared (IR) cutoff, L ¼ ðαH_ þ βH2Þ−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 literature, do not give analytically ω ¼ ωðzÞ and q ¼ qðzÞ. 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 ≈ 0.6. Then we suggest a correspondence between the quintessence and tachyon scalar fields and HDE in the framework of the DGP braneworld. This correspondence allows us to reconstruct the evolution of the scalar fields and the scalar potentials. We also investigate the stability of the presented model by calculating the squared sound speed, v2s , whose sign determines the stability of the model. Our study shows that v2s could be positive provided the parameters of the model are chosen suitably. In particular, for α > 1, β > 0, and α < 1, β < 0, we have v2s > 0 during the history of the Universe, and so the stable dark-energydominated 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.
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