Theoretical analysis on the Rényi holographic dark energy in the fractal cosmology

Abstract

In this paper, we investigate the Rényi holographic dark energy model with the interaction between dark energy and dark matter within the framework of the fractal cosmology in which the Hubble horizon is considered as the IR cutoff. In this setting, we derive the evolution equation of the Rényi holographic dark energy density parameter, the equation of state (EoS) parameter and deceleration parameter. We find that the model in the fractal cosmology can explain the accelerated expansion of the universe. In addition, we discuss the statefinder diagnosis of this model, plotting the curves of [Formula: see text] and [Formula: see text] with redshift [Formula: see text] and the evolutionary trajectories of [Formula: see text]. We find that statefinder can ideally break the degeneracy of different coupling parameter values in this model. Moreover, we find that the statefinder pair [Formula: see text] performs better than [Formula: see text] and [Formula: see text] in this model.