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Using f(T) gravitational theory, we construct modified cosmological models via the first law of thermodynamics by using the non-extensive thermodynamics framework, the effects of which are captured by the parameter δ. The resulting cosmological equations are modified compared to the standard Einstein-Hilbert ones, with the modifications coming from the f(T) gravitational theory and from the non-extensive parameter which quantifies the non-extensive thermodynamics effects quantified by the parameter δ, which when is set equal to unity, one recovers the field equations of f(T) gravity. We study in detail the cosmological evolution of the model in the presence of collisionless non-relativistic matter case, and we derive the exact forms of the dark energy density parameter and of the dark energy equation of state parameter, from which we impose constraints on the non-extensive thermodynamics parameter, δ, by using the Planck 2018 data on cosmological parameters. Accordingly, we repeat our calculations after including the relativistic matter along with the non-relativistic one, and we derive the new forms of the dark energy density parameter and of the dark energy equation of state parameter. Our study shows that the inclusion of non-extensive thermodynamic effects, quantified by the parameter δ, for a flat Friedmann-Robertson-Walker Universe, has measurable differences compared with the normal thermodynamics case. We confront our results with Type Ia supernovae observations for z≥0.4 and we obtain reasonably agreement with the observational data.

Non-Extensive Thermodynamics Effects in the Cosmology of f(T) Gravity