$f(R)$ gravity with Torsion and the Immirzi field: signature for GW detection

We propose a Nieh-Yan extension of f ® models in the presence of Immirzi field and the resulting theory is studied in the context of first order formalism. We claim as in our model the ambiguities related to the Palatini vacuum case are solved, allowing us to extend the range of applicability of the method proposed in [4] to a wider class of f ® theories. In particular we analyze within such a theoretical framework the propagation of gravitational waves in vacuum and outline as a dynamical Immirzi field could be regarded as a propagating torsion field with non-trivial and detectable effects on standard gravitational polarizations.