Conformal transformation in f(T) theories

It is well known that f ( R ) theories are dynamically equivalent to a particular class of scalar-tensor theories. In analogy to the f ( R ) extension of the Einstein-Hilbert action of general relativity, f ( T ) theories are generalizations of the action of teleparallel gravity. The field equations are always second order, remarkably simpler than f ( R ) theories. It is interesting to investigate whether f ( T ) theories have the similar conformal features possessed in f ( R ) theories. It is shown, however, that f ( T ) theories are not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation, since there appears an additional scalar-torsion coupling term. We discuss briefly what constraint of this coupling term may be put on f ( T ) theories from observations of the solar system.