The distinctions between $\Lambda$CDM and $f(T)$ gravity according Noether symmetry

Understand

Noether's theory offers us a useful tool to research the conserved quantities and symmetries of the modified gravity theories, among which the $f(T)$ theory, a generally modified teleparallel gravity, has been proposed to account for the dark energy phenomena.

• By the Noether symmetry approach, we investigate the power-law, exponential and polynomial forms of $f(T)$ theories.
• All forms of $f(T)$ concerned in this work possess the time translational symmetry, which is related with energy condition or Hamilton constraint.
• In addition, we find out that the performances of the power-law and exponential forms are not pleasing.