Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and Dark Matter Freeze-out

We consider Tsallis cosmology as an approach to thermodynamic gravity and derive the bound on the Tsallis parameter to be $beta<2$ by using the constraints derived from the formation of the primordial light elements, Helium, Deuterium and Litium, from the observational data from Big Bang Nucleosynthesis (BBN) which allows only a very tiny deviation from General Relativity (GR). Next we consider thermal dark matter (DM) freeze-out mechanism in Tsallis cosmological era and derive bounds on the Tsallis parameter from the observed DM relic abundance to be $1-beta < 10^{-5}$.