The Immirzi parameter from an external scalar field

Abstract

We promote the Immirzi parameter to be a minimally coupled scalar field and we analyzed the Hamiltonian constraints in the framework of Loop Quantum Gravity without the time gauge. Proper SU(2) connections can be defined and a term containing derivatives of the field $\beta$ enters into their definition. Furthermore, boost degrees of freedom are non-dynamical, while the super-momentum constraints coincide with the scalar field case. Hence, the kinematical Hilbert space can be defined as for gravity in presence of a minimally coupled scalar field. Then, we analyzed the dynamical implications of this scenario and we outlined how a the dynamical relaxation to a non-vanishing vacuum expectation value is predicted.

5 pages

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• Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
• $f(R)$ gravity with Torsion and the Immirzi field: signature for GW detection
• Gauge invariant coupling of fields to torsion: a string inspired model
• Gravity in presence of fermions as a SU(2) gauge theory
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