Noether symmetry in f(T) teleparallel gravity

Abstract

Noether symmetry in teleparallel f(T) gravity, where T is the torsion scalar, has been studied in the background of Robertson–Walker space–time. It is found that Noether symmetry admits f(T)∝T32 and the associated conserved current is Σ=aa˙T12, in matter dominated era. In the process, the recent claim by Wei et al. [1] that Noether symmetry admits f(T)∝Tn, (where n is an arbitrary constant) is found not to be correct, since the conserved current satisfies the field equations only for a special choice of n=32. Further, correspondence between f(R) and f(T) theories of gravity has also been established.