  The role of torsion and a scalar field $\phi$ in gravitation, especially, in
the presence of a Dirac field in the background of a particular class of the
Riemann-Cartan geometry is considered here. Recently, a Lagrangian density with
Lagrange multipliers has been proposed by the author which has been obtained by
picking some particular terms from the SO(4,1) Pontryagin density, where the
scalar field $\phi$ causes the de Sitter connection to have the proper
dimension of a gauge field. In this formalism, conserved axial vector matter
current can be constructed, irrespective of any gauge choice, in any manifold
having arbitrary background geometry. This current is not a Noether current.
