LAUSR

We apply the holographic principle in the cosmological context through the nonextensive Tsallis entropy, used to describe the thermodynamic properties of nonstandard statistical systems such as the gravitational ones. Assuming the future event horizon as the infrared cutoff, we build a dark energy model free from cosmological inconsistencies, which includes standard thermodynamics and standard holographic dark energy as a limiting case. We thus describe the dynamics of Tsallis holographic dark energy in a flat FLRW background. Hence, we investigate cosmological perturbations in the linear regime on sub-horizon scales. We study the growth of matter fluctuations in the case of clustering dark matter and a homogeneous dark energy component. Furthermore, we employ the most recent late-time cosmic data to test the observational viability of our theoretical scenario. We thus obtain constraints on the free parameters of the model by means of Monte Carlo numerical method. We also used Bayesian selection criteria to estimate the statistical preference for Tsallis holographic dark energy compared to the concordance $\Lambda$CDM paradigm. Our results show deviations from standard holographic dark energy within the $2\sigma$ confidence level. Finally, the analysis of the dark energy equation of state indicates a quintessence-like behaviour with no evidence for phantom-divide crossing at the $1\sigma$ level.