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The role of torsion and a scalar field $\phi$ in gravitation in thebackground of a particular class of the Riemann-Cartan geometry is consideredhere. Some times ago, a Lagrangian density with Lagrange multipliers has beenproposed by the author which has been obtained by picking some particular termsfrom the SO(4,1) Pontryagin density, where the scalar field $\phi$ causes thede Sitter connection to have the proper dimension of a gauge field. Here it hasbeen shown that the divergence of the axial torsion gives the Newton's constantand the scalar field becomes a function of the Ricci scalar $\mathcal{R}$. Thestarting Lagrangian then reduces to a Lagrangian representing the metric$f(\mathcal{R})$ gravity theory.

Torsion, Scalar Field and f(\mathcal{R}) Gravity