Dynamical behavior in $f(T,T_G)$ cosmology

Abstract

The $f(T,T_G)$ class of gravitational modification, based on the quadratic torsion scalar $T$, as well as on the new quartic torsion scalar $T_G$ which is the teleparallel equivalent of the Gauss-Bonnet term, is a novel theory, different from both $f(T)$ and $f(R,G)$ ones. We perform a detailed dynamical analysis of a spatially flat universe governed by the simplest non-trivial model of $f(T,T_G)$ 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 to a dark energy - dark matter scaling solution, and 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.

arXiv comment23 pages, 6 figures, matches the version published in CQG

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• f(T) teleparallel gravity and cosmology
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• $f(T,\mathcal{T})$ gravity and cosmology
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• Autonomous Dynamical System Approach for $f(R)$ Gravity
• Testing wormhole solutions in extended gravity through the Poynting-Robertson effect
• Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology
• New observational constraints on $f(R)$ gravity from cosmic chronometers
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• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
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