Conformal transformation in $f(T)$ theories

Understand

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.