  The Immirzi parameter is promoted to be a scalar field and the Hamiltonian
analysis of the corresponding dynamical system is performed in the presence of
gravity. We identified some SU(2) connections, generalizing Ashtekar-Barbero
variables, and we rewrite the constraints in terms of them, setting the
classical formulation suitable for loop quantization. Then, we consider the
reduced system obtained when restricting to a flat isotropic cosmological
model. By mimicking loop quantization via an effective semiclassical treatment,
we outline how quantum effects are able to tame the initial singularity both in
synchronous time and when the Immirzi field is taken as a relational time.
