Abstract:
In this article, we investigate the modified F (T ) gravity, which is non-minimally coupled with the Dirac field
in Friedman-Robertson-Walker space-time. Point-like Lagrangian is derived and modified Friedmann equations and Dirac
equations for the fermion field are obtained 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 value for this model are determined. Cosmological solutions that have a power form and describe the late time
accelerated expansion of the Universe are obtained. The Hubble parameter, pressure and energy density for the Dirac field
and the equation of state parameter are found.
