Conformal transformations in modified teleparallel theories of gravity revisited

It is well known that one cannot apply a conformal transformation to f(T) gravity to obtain a minimally coupled scalar field model, and thus no Einstein frame exists for f(T) gravity. Furthermore nonminimally coupled teleparallel dark energy models are not conformally equivalent to f(T) gravity. However, it can be shown that f(T) gravity is conformally equivalent to a teleparallel phantom scalar field model with a nonminimal coupling to a boundary term only. In this work, we extend this analysis by considering a recently studied extended class of models, known as f(T, B) gravity, where B is a boundary term related to the divergence of a contraction of the torsion tensor. We find that nonminimally coupled teleparallel dark energy models are conformally equivalent to either an f(T, B) or f(B) gravity model. Finally conditions on the functional form of f(T, B) gravity are derived to allow it to be transformed to particular nonminimally coupled scalar field models.