Growth factor in teleparallel Gauss-Bonnet gravity

Teleparallel gravity offers a competing geometric framework on which to build cosmological models. The Gauss-Bonnet invariant captures key aspects of the underlying geometry that has been shown to be an interesting way to form cosmological models beyond $\mathrm{\Lambda }$CDM cosmology. In this work, we explore three competing cosmological models in $F(T,T_G)$ cosmology in the context of their evolution of the growth of structure in the Universe. This is a core test of the viability of any cosmological model. In our work, we show how these models are qualitatively competitive with $\mathrm{\Lambda }$CDM cosmology for certain ranges of model parameters. Interestingly, the models can arrive at the same level of growth as $\mathrm{\Lambda }$CDM while producing possible deviations at intermediate scales.