# Studying the Intervention of an Unusual Term in $f(T)$ Gravity via Noether Symmetry

## TL;DR

This paper introduces a novel term in $f(T)$ gravity involving a scalar field and its derivatives, analyzed via Noether symmetry, showing it aligns with observational data and supports late-time cosmic acceleration.

## Contribution

The study proposes and investigates a new coupling term in $f(T)$ gravity, demonstrating its consistency and potential to explain late-time acceleration without anomalies.

## Key findings

- The new term does not cause anomalies in the theory.
- Numerical solutions match observational data on cosmic acceleration.
- The term supports late-time accelerated expansion in $f(T)$ gravity.

## Abstract

As usual, we observe an unknown coupling function, i.e. $F(\varphi)$, with a function of torsion and also curvature, i.e. $f(T)$ and $f(R)$, generally depending on a scalar field. In $f(R)$ case, it comes from quantum correlations and other reasons. Now, what if beside this term in $f(T)$-gravity context, we enhance the action through another term which depends on both scalar field and its derivatives? In this paper, we have added such an unprecedented term in the generic common action of $f(T)$-gravity such that in this new term, an unknown function of torsion has coupled with an unknown function of both scalar field and its derivatives. We have explained why we can append such term, in the introduction in details. By the use of Noether symmetry approach, we have considered its behavior and effect. We have shown that it does not produce an anomaly, but rather it works successfully and numerical analysis of the exact solutions of field equations coincide with all most important observational data particularly late-time-accelerated expansion. So, this new term may be added to the gravitational actions of $f(T)$-gravity.