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We investigate the Tsallis holographic dark energy (THDE) models in the context of perturbations growth. We assume the description of dark energy by considering the holographic principle and the nonadditive entropy to carry out this. We implement the perturbed relativistic equations to achieve the growth of matter fluctuations, being the growth rate of the cosmic structures is non-negligible at low redshifts. To constrain and compare the models, we carry out the Bayesian analysis using the recent geometrical and growth rate observational data. The main results are: (i) the models are compatible with cosmological observations, (ii) the cosmological constant recovered with a $1sigma$ confidence level, furthermore (iii) they could cross the phantom barrier. Finally, the models can relieve $approx 1sigma$ the $sigma_8$ tension in the non-clustered case and can alleviate in $approx 2.8sigma$ the $H_0$ tension. From the model selection viewpoint, the data discarded the THDE models.
We study some cosmological features of Tsallis holographic dark energy (THDE) in Cyclic, DGP and RS II braneworlds. In our setup, a flat FRW universe is considered filled by a pressureless source and THDE with the Hubble radius as the IR cutoff, whil
In order to apply holography and entropy relations to the whole universe, which is a gravitational and thus nonextensive system, for consistency one should use the generalized definition for the universe horizon entropy, namely Tsallis nonextensive e
Using the Tsallis generalized entropy, holographic hypothesis and also considering the Hubble horizon as the IR cutoff, we build a holographic model for dark energy and study its cosmological consequences in the Brans-Dicke framework. At first, we fo
It has been found that the geometrical diagnostic methods can break the degeneracy for dark energy models. In this paper, we investigate the $Om$ diagnostic, the statefinder hierarchy $S_{n}$ and the composite null diagnostic ${S_{n},epsilon}$ for th
We constrain the contribution of tensor-mode perturbations with free $n_t$ in the models with dynamical dark energy with the barotropic equation of state using Planck-2015 data on CMB anisotropy, polarization and lensing, BICEP2/Keck Array data on B-