  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 article the scalar field has been linked to
the dimension of the Dirac field. Here we get the field equations for the Dirac
field and the scalar field in such a way that both of them appear to be
mutually non-interacting. In this scenario the scalar field appears to be a
natural candidate for the dark matter and the dark radiation.
