Dynamical behavior in f(T, TG) cosmology

The class of gravitational modification, based on the quadratic torsion scalar T as well as on the new quartic torsion scalar TG, which is the teleparallel equivalent of the Gauss–Bonnet term, is a novel theory, different from both f (T) and ones. We perform a detailed dynamical analysis of a spatially flat universe governed by the simplest non-trivial model of gravity which does not introduce a new mass scale. We find that the universe can result in dark-energy dominated, quintessence-like, cosmological-constant-like, or phantom-like solutions, according to the parameter choices. Additionally, it may result in a dark energy–dark matter scaling solution; thus it can alleviate the coincidence problem. Finally, the analysis 'at infinity' reveals that the universe may exhibit future, past, or intermediate singularities, depending on the parameters.

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