Noether Symmetry Approach in Scalar-Torsion $f(T,\phi)$ Gravity

TL;DR

This paper applies the Noether symmetry approach to scalar-torsion $f(T,)$ gravity, deriving exact cosmological solutions that exhibit accelerated expansion and align with current observational data.

Contribution

It introduces a method to determine the form of $f(T,)$ and find exact solutions in scalar-torsion gravity using Noether symmetries, advancing model-building in modified gravity.

Findings

Derived exact cosmological solutions consistent with accelerated expansion.

Obtained present-day cosmological parameters matching observations.

Demonstrated the utility of Noether symmetry in constraining $f(T,)$ models.

Abstract

The Noether Symmetry approach is applied to study an extended teleparallel $f(T,\phi)$ gravity that contains the torsion scalar $T$ and the scalar field $\phi$ in the context of an Friedmann-Lema\^{i}tre-Robertson-Walker space-time. We investigate the Noether symmetry approach in $f(T,\phi)$ gravity formalism with the specific form of $f(T,\phi)$ and analyze how to demonstrate a nontrivial Noether vector. The Noether symmetry method is a helpful resource for generating models and finding out the exact solution of the Lagrangian. In this article, we go through how the Noether symmetry approach enables us to define the form of the function $f(T,\phi)$ and obtain exact cosmological solutions. We also find the analytical cosmological solutions to the field equations, that is consistent with the Noether symmetry. Our results demonstrate that the obtained solutions enable an accelerated expansion of the Universe. We have also obtained the present value of the Hubble parameter, deceleration parameter, and effective equation of state parameter, which is fit in the range of current cosmological observations.