In this paper we study cosmological solutions of the f(T, B) gravity using dynamical system analyses. For this purpose, we consider cosmological viable functions of f(T, B) that are capable of reproducing the dynamics of the Universe. We present three specific models of f(T, B) gravity which have a general form of their respective solutions by writing the equations of motion as an autonomous system. Finally, we study its hyperbolic critical points and general trajectories in the phase space of the resulting dynamical variables which turn out to be compatible with the current late-time observations.

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In light of the statistical performance of cosmological observations, in this work we present the cosmography in f(T,B) gravity. In this scenario we found a cosmological viable standard case that allows the reduction of the degeneracy between several f(T,B) models already proposed in the literature. Furthermore, we constrain this model using Pantheon SNeIa compilation, cosmic chronometers and a newly GRB calibrated data sample. We found that with an appropriate strategy for including the cosmographic parameter, we do produce a viable cosmology with our model within f(T,B) gravity.

In this paper, we explore the possibility to find exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lemaître–Tolman–Bondi (LTB) dust models. We apply to the LTB metric the formalism of Teleparallel Gravity in its extension to [Formula: see text] models, which can be seen as the analagous from the Schwarzschild solution in General Relativity. An exact LTB solution is obtained which is compatible with a specific [Formula: see text] model whose observational constraints are cosmologically viable in a standard spatially flat Robertson–Walker geometry.