Constraints on Tsallis cosmology using recent low and high redshift measurements

Recently Tsallis cosmology has been presented as a novel proposal for alleviating both $H_0$ and $\sigma_8$ tensions. Hence a universe filled with matter and radiation as perfect fluids and considering the Tsallis entropy is confronted using recent cosmological measurements coming from cosmic chronometers, type Ia supernovae, hydrogen II galaxies, quasars, and baryon acoustic oscillations. Following a Bayesian Monte Carlo Markov Chain analysis and combining the samples, we constrain the main characteristic parameters $\alpha = 1.031^{+0.054}_{-0.051}$ and $\delta = 1.005^{+0.001}_{-0.001}$ where the uncertainties are $1\sigma$ confidence level. Additionally, we estimate the current deceleration parameter $q_0=-0.530^{+0.018}_{-0.017}$, the deceleration-acceleration transition redshift $z_T=0.632^{+0.028}_{-0.028}$ and the age of the universe $\tau_U = 12.637^{+0.067}_{-0.066}\,\rm{Gyrs}$ which are in agreement with the standard cosmology ($\Lambda$CDM) within $1.5\sigma$. Furthermore, we find that the dark energy equation of state is consistent with both phantom and quintessence behaviors within $1\sigma$ in the past and converging to $\Lambda$CDM in the future. Additionally, we find agreement values of $H_0$ within $1\sigma$ with the SH0ES values when the CMB distance priors are added to the analysis, suggesting that $H_0$ tension could be alleviated. Finally, Tsallis cosmology is preferred over $\Lambda$CDM by the combined data that motives further studies at the perturbation level.