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

TL;DR

This paper investigates the dynamical behavior of a novel $f(T,T_G)$ gravity model, revealing diverse cosmological solutions including dark energy, quintessence, and singularities, thus offering insights into cosmic evolution and the coincidence problem.

Contribution

It introduces and analyzes a new $f(T,T_G)$ gravity model, providing a detailed dynamical analysis and exploring its potential to explain various cosmic phenomena.

Findings

Universe can be dark-energy dominated, quintessence-like, or phantom-like.

The model can produce dark energy-dark matter scaling solutions.

Future, past, or intermediate singularities are possible depending on parameters.

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.