$$O\left( d,d\right) $$ symmetry in teleparallel dark energy

An important characteristic of the dilaton cosmological model is the Gasperini–Veneziano duality transformation which follows from the existence of the $$O\left( d,d\right) $$ symmetry. In this study, we consider the equivalent dilaton theory in teleparallel dark energy with the $$O\left( d,d\right) $$ symmetry, while the equivalent teleparallel-duality transformation is presented. The classical solution of the field equations is derived. Finally, the Wheeler–DeWitt equation of quantum cosmology is discussed.