Noether symmetry in f ( T ) teleparallel gravity

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 ) ∝ T 3 2 and the associated conserved current is Σ = a a ˙ T 1 2 , in matter dominated era. In the process, the recent claim by Wei et al. [1] that Noether symmetry admits f ( T ) ∝ T n , (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 = 3 2 . Further, correspondence between f ( R ) and f ( T ) theories of gravity has also been established.