Holographic dark energy from nonadditive entropy: cosmological
  perturbations and observational constraints
  We apply the holographic principle in the cosmological context through the
nonadditive 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.
