# Noether symmetry in $f(T)$ teleparallel gravity

## TL;DR

This paper clarifies the form of $f(T)$ in teleparallel gravity compatible with Noether symmetry, correcting previous claims and showing that only $f(T) \\propto T^{3/2}$ admits a conserved current consistent with field equations.

## Contribution

It demonstrates that the only $f(T)$ form compatible with Noether symmetry and field equations is proportional to $T^{3/2}$, correcting earlier misconceptions.

## Key findings

- Only $f(T) \\propto T^{3/2}$ admits a conserved current.
- Previous claim of $f(T) \\propto T^{n}$ for arbitrary $n$ is incorrect.
- The conserved current is $a \\dot a T^{1/2}$.

## Abstract

Hao Wei et.al. has claimed in $\mathrm{Phys. Lett. \textbf{B707}, 298 (2012)}$ that Noether symmetry in the context of teleparallel $f(T)$ theory of gravity admits $f(T)\propto T^{n}$, (where $n$ is an arbitrary) in matter domain era in Friedmann- Robertson universe. But, it has been shown that the conserved current obtained under the process does not satisfy the field equations in general. Here, it is shown that Noether Symmetry admits $f(T)\propto T^\frac{3}{2}$ along with a conserved current $ a \dot a T^\frac{1}{2}$ in teleparallel $f(T)$ gravity. Thus, their claim is not correct.