Non-flat and non-extensive thermodynamic effects of Møller tetradic theory of gravitation on cosmology

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We derive non-flat cosmological models for two cases (i.e., dust and radiation) in the context of Møller’s tetradic theory (MTT) of gravitation using the tetrad that creates the non-flat Friedmann–Robertson–Walker (FRW) metric. These two models are affected by the free dimensional parameter, λ, that characterized MTT, which approaches zero in the flat case for both models. Using standard definitions of thermodynamics, we calculate the radius horizon, Hawking temperature, and entropy of our non-flat models in the framework of cosmology and show the effect of λ on open and closed universes. We then use the first law of thermodynamics to construct non-flat cosmological models via the non-extensive thermodynamic approach. The resulting models are affected by λ and the extensive parameter, δ, which quantifies the effect of non-extensive thermodynamics. When we set, λ=0 and δ=1, we return to Einstein’s general relativity models. We study the evolution of our models in the presence of collisionless non-relativistic matter and describe precise forms of the dark energy density and equation-of-state parameter constraining the non-extensive thermodynamic parameter. We show that insertion of the non-extensive thermodynamic parameter affects the non-flat FRW universe in a manner that noticeably differs from that observed under normal thermodynamics. We also show that the deceleration of the open universe behaves as dark energy in a future epoch, i.e., when the redshift approaches −1, i.e., z≈−1.