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

Understand

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.