Cosmological applications of $F(T,T_G)$ gravity
  We investigate the cosmological applications of $F(T,T_G)$ gravity, which is
a novel modified gravitational theory based on the torsion invariant $T$ and
the teleparallel equivalent of the Gauss-Bonnet term $T_{G}$. $F(T,T_{G})$
gravity differs from both $F(T)$ theories as well as from $F(R,G)$ class of
curvature modified gravity, and thus its corresponding cosmology proves to be
very interesting. In particular, it provides a unified description of the
cosmological history from early-times inflation to late-times
self-acceleration, without the inclusion of a cosmological constant. Moreover,
the dark energy equation-of-state parameter can be quintessence or
phantom-like, or experience the phantom-divide crossing, depending on the
parameters of the model.
