Abstract:
In this article, we investigate the modified F(T) gravity, which is non-minimally
coupled with the Dirac (fermion) field in Friedmann-Robertson-Walker space-time. Point-like
Lagrangian is derived and modified Friedmann equations and Dirac equations for the fermion
field are obtained by using the Lagrange multiplier. The Noether symmetry method related to
differential equations is a useful tool for studying conserved quantities. In addition, this method
is very useful for determining the unknown functions that exist in the point-like Lagrangian.
Using this method, the form of the coupling between gravity and matter, the self-consistent
potential, the symmetry generators, the form of F(T) gravity and the first integral (Noether
charge) or a conserved quantity for this model are determined. Cosmological solutions that have
a power-law form and describe the late time accelerated expansion of the Universe are obtained.
