Cosmological Perturbations in the Tsallis Holographic Dark Energy Scenarios

The Tsallis Holographic Dark Energy (THDE) models are investigated in the context of growth of perturbations. To carry out this, we assume the description of dark energy considering the holographic principle and the nonadditive entropy. 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. In order to constrain and to compare the models, we carry out the Bayesian analysis by using the recent geometrical and growth rate observational data. These models are compatible with cosmological observations, can cross the phantom barrier, and the cosmological constant is recovered with a $1\sigma$ confidence level. The models can relieve in $\approx 1\sigma$ the $\sigma_8$ tension in the non-clustered case, and can alleviate in $\approx 2\sigma$ the $H_0$ tension. From the model selection viewpoint, the THDE models are discarded by the data