Acceleration of the Universe without the Hubble tension with Kaniadakis holographic dark energy using the Hubble horizon as the IR cut-off

In this paper, we introduce a holographic dark energy model that incorporates the first-order approximate Kaniadakis entropy, utilizing the Hubble horizon, [Formula: see text], as the infrared cutoff. We investigate the cosmological evolution within this framework. The model introduces an extra parameter relative to the [Formula: see text]CDM model. It posits a Universe that is initially dominated by dark matter, which then evolves to a phase where dark energy becomes the predominant component, with this transition occurring at a redshift of approximately [Formula: see text]. The energy density of dark energy is ultimately expected to become constant, thereby circumventing the potential issue of a “big rip”. Employing the most recent Type Ia supernova and Hubble parameter data, we constrain the model’s parameters and find a Hubble constant of [Formula: see text] km/s/Mpc, thereby resolving the Hubble tension issue. The estimated age of the Universe, based on the best-fit parameter values, is [Formula: see text] Gyr. Furthermore, we predict the number of strong gravitational lenses and conduct statefinder and [Formula: see text] diagnostic analyses to validate and characterize the model.