Noether Gauge Symmetry of Modified Teleparallel Gravity Minimally Coupled with a Canonical Scalar Field

TL;DR

This paper explores Noether gauge symmetries in a modified teleparallel gravity model with a scalar field, identifying invariants and showing the model's potential to mimic the ΛCDM cosmology.

Contribution

It explicitly determines the functions in the $f(T)$ gravity model with a scalar field and identifies conserved quantities, providing a new approach to alternative cosmological models.

Findings

Two invariants identified, including energy conservation and scaling invariance.

The model's Hubble parameter behavior closely matches ΛCDM.

The equation of state parameter can cross the cosmological constant boundary.

Abstract

This paper is devoted to the study of Noether gauge symmetries of $f(T)$ gravity minimally coupled with a canonical scalar field. We explicitly determine the unknown functions of the theory $f(T),V(\phi), W(\phi)$. We have shown that there are two invariants for this model, one of which defines the Hamiltonian $H$ under time invariance (energy conservation) and the other is related to scaling invariance. We show that the equation of state parameter in the present model can cross the cosmological constant boundary. The behavior of Hubble parameter in our model closely matches to that of $\Lambda$CDM model, thus our model is an alternative to the later.