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We derive non-flat cosmological models for two cases (i.e., dust andradiation) in the context of M{\o}ller's tetradic theory (MTT) of gravitationusing the tetrad that creates the non-flat Friedmann-Robertson-Walker (FRW)metric. These two models are affected by the free dimensional parameter,$\lambda$, that characterized MTT, which approaches zero in the flat case forboth models. Using standard definitions of thermodynamics, we calculate theradius horizon, Hawking temperature, and entropy of our non-flat models in theframework of cosmology and show the effect of $\lambda$ on open and closeduniverses. We then use the first law of thermodynamics to construct non-flatcosmological models via the non-extensive thermodynamic approach. The resultingmodels are affected by $\lambda$ and the extensive parameter, $\delta$, whichquantifies the effect of non-extensive thermodynamics. When we set, $\lambda=0$and $\delta=1$, we return to Einstein's general relativity models. We study theevolution of our models in the presence of collisionless non-relativisticmatter and describe precise forms of the dark energy density andequation-of-state parameter constraining the non-extensive thermodynamicparameter. We show that insertion of the non-extensive thermodynamic parameteraffects the non-flat FRW universe in a manner that noticeably differs from thatobserved under normal thermodynamics. We also show that the deceleration of theopen universe behaves as dark energy in a future epoch, i.e., when the redshiftapproaches -1, i.e., $z\approx$-1.

Non-flat and non-Extensive Thermodynamic Effects of M{\o}ller tetradic theory of gravitation on cosmology