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ABSTRACT We describe a general constitutive framework for a teleparallel extension of the general theory of relativity. This approach goes beyond the teleparallel equivalent of general relativity (TEGR) by broadening the analogy with the electrodynamics of media. In particular, the main purpose of this paper is to investigate in detail a local constitutive extension of TEGR that is the local limit of non-local gravity. Within this framework, we study the modified Friedmann–Lemaître–Robertson–Walker cosmological models. Of these, the most cogent turns out to be the modified Cartesian flat model which is shown to be inconsistent with the existence of a positive cosmological constant. Moreover, dynamic dark energy and other components of the modified Cartesian flat model evolve differently with the expansion of the universe as compared to the standard flat cosmological model. The observational consequences of the modified Cartesian flat model are briefly explored and it is shown that the model is capable of resolving the H0 tension.
Tabatabaei et al. (Thu,) studied this question.