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 enters into their definition. Furthermore, boost degrees of freedom are nondynamical, while the supermomentum 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 outline how a dynamical relaxation to a nonvanishing vacuum expectation value is predicted, so recovering the standard loop quantum gravity formulation.

f(R) gravity with torsion and the Immirzi field: Signature for gravitational wave detection

“…We conclude this section noting that the same results could be obtained even if we substituted the relations (22) at lagrangean level. Furthermore, to solve simultaneously (25) and (26), assuming that we have solve (24) for R, is in general an highly non-trivial task also for simple f (R) models. It motivated us to seek for simpler scenarios, as those the linearized theory can offer, with the aim of investigating new effects in gravitational waves propagation due to the Immirzi field.…”

Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity

“…While this somewhat unexpected theoretical ambiguity has persisted, to date the mainstream view seems to be taking a "pragmatic" approach by fixing β [21] to phenomenologically match the black hole entropies predicted by the resulting LQG with the Bekenstein-Hawking values. However, some felt such a practice unnatural as exemplified by Rovelli's opinion that "the result is not entirely satisfactory," remarking "the sense that there is something important which is not yet understood is unavoidable" [2], while some others have developed models with the Immirzi parameter turned into a scalar field [22][23][24]. Given gradually impending contact of LQG with the real world [1,2] and increased understanding of quantum gravity effects such as decoherence through the emission and absorption of gravitons [25][26][27][28][29][30], the physical ramifications of the Immirzi parameter on spacetime fluctuations towards the deep Planckian domain have been receiving ever more interest and attention [31].…”

Big-bounce cosmology in the presence of Immirzi field

“…Here, we address the point of view to treat such a Immirzi variable as a real field [13][14][15][16][17], whose evolution has to be somehow implemented and hopefully accounts for the emergence of a given constant value.…”

“…In order to tame this un-wanted feature, some approaches have been developed in which the Immirzi parameter is promoted to be a dynamical scalar field [13][14][15][16][17].…”

“…where (β) F i ab is the SU (2) field strength of (β) A i a . It is worth noting that the vector constraint (13) retains the same form as in Holst formulation in the presence of a minimally coupled scalar field (see [26,27]). On the contrary, the scalar constraint contains some additional terms.…”