  In Loop Quantum Gravity the classical point of departure is the
Einstein-Hilbert action modified by the addition of the so-called Holst term.
Classically, this term does not affect the equations of motion, but it induces
a well-known quantization ambiguity in the quantum theory, parametrized by the
Barbero--Immirzi parameter. Recently, it has been suggested to promote the
Barbero--Immirzi parameter to a field. The resulting theory, obtainable
starting from the usual Holst action, is General Relativity coupled to a
pseudo-scalar field. However, this theory turns out to have an unconventional
kinetic term for the BI field and a rather unnatural coupling with fermions.
The main goal of this work is twofold: Firstly, to propose a further
generalization of the Holst action, which yields a theory of gravity and matter
with a more natural coupling to the Barbero--Immirzi field; secondly, to study
the possible implications for cosmology correlated to the existence of this new
pseudo-scalar field.
