Constraints on Tsallis cosmology using recent low and high redshift measurements

Recently Tsallis cosmology has been presented as a novel proposal for alleviating both H₀ and σ₈ 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 α = 1.031+0.054-0.051 and δ = 1.005+0.001-0.001 where the uncertainties are 1σ confidence level. Additionally, we estimate the current deceleration parameter q₀=-0.530+0.018-0.017, the deceleration-acceleration transition redshift zT=0.632+0.028-0.028 and the age of the universe τU = 12.637+0.067-0.066\,Gyrs which are in agreement with the standard cosmology (ΛCDM) within 1.5σ. Furthermore, we find that the dark energy equation of state is consistent with both phantom and quintessence behaviors within 1σ in the past and converging to ΛCDM in the future. Additionally, we find agreement values of H₀ within 1σ with the SH0ES values when the CMB distance priors are added to the analysis, suggesting that H₀ tension could be alleviated. Finally, Tsallis cosmology is preferred over ΛCDM by the combined data that motives further studies at the perturbation level.