Giovanni Montani

Towards Loop Quantum Gravity without the Time Gauge

The Hamiltonian formulation of the Holst action is reviewed and it provides a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the loop quantum gravity quantization procedure can be applied when the time-gauge condition does not stand.

Implications of non-analytical f(R) gravity at Solar-System scales

We motivate and analyze the weak-field limit of a non-analytic modification of the Einstein–Hilbert Lagrangian for the gravitational field. After investigating the parameter space of the model, we impose constraints on the parameters characterizing this class of theories by means of solar system data, i.e. we establish the validity range where this solution applies and refine the constraints by comparison with planetary orbits. As a result, we claim that this class of models is viable within different astrophysical scales.

The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. In this way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.

Shortcomings of the big bounce derivation in loop quantum cosmology

We give a prescription to define in loop quantum gravity the electric field operator related to the scale factor of a homogeneous and isotropic cosmological space-time. This procedure allows us to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in loop quantum cosmology. This feature makes the super-Hamiltonian regularization an open issue of the whole formulation.

Squeezing of toroidal accretion disks

Accretion disks around very compact objects such as very massive black holes can grow according to thick toroidal models. We face the problem of defining how the thickness of a toroidal accretion disk spinning around a Schwarzschild black hole changes under the influence of a toroidal magnetic field and by varying the fluid angular momentum. We consider both a hydrodynamic and a magnetohydrodynamic disk based on the Polish doughnut thick model. We show that the torus thickness remains basically unaffected but tends to increase or decrease slightly depending on the balance of the magnetic, gravitational and centrifugal effects which the disk is subjected to.

Immirzi parameter from an external scalar field

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

Polymer quantum dynamics of the Taub universe

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Spin connection as Lorentz gauge field in Fairchild’s action

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.

Nonsingular cosmology from evolutionary quantum gravity

Within the framework of nonstandard (Weyl) representations of the canonical commutation relations, we investigate the polymer quantization of the Taub cosmological model. The Taub model is analyzed within the Arnowitt-Deser-Misner reduction of its dynamics, by which a time variable arises. While the energy variable and its conjugate momentum are treated as ordinary Heisenberg operators, the anisotropy variable and its conjugate momentum are represented by the polymer technique. The model is analyzed at both classical and quantum level. As a result, classical trajectories flatten with respect to the potential wall, and the cosmological singularity is not probabilistically removed. In fact, the dynamics of the wave packets is characterized by an interference phenomenon, which, however, is not able to stop the evolution towards the classical singularity.

Non-analytical power-law correction to the Einstein–Hilbert action: Gravitational wave propagation

We propose a modified gravitational action containing besides the Einstein–Cartan term some quadratic contributions resembling the Yang–Mills Lagrangian for the Lorentz spin connections. We outline how a propagating torsion arises and we solve explicitly the linearized equations of motion on a Minkowski background. We identify among torsion components six degrees of freedom: one is carried by a pseudo-scalar particle, five by a tachyon field. By adding spinor fields and neglecting backreaction on the geometry, we point out how only the pseudo-scalar particle couples directly with fermions, but the resulting coupling constant is suppressed by the ratio between fermion and Planck masses. Including backreaction, we demonstrate how the tachyon field provides causality violation in the matter sector, via an interaction mediated by gravitational waves.