arXiv subjects

Giovanni Montani

Publications and source records attributed to Giovanni Montani.

At least 199 records · Page 11Linked to original sources

arXiv2008

Classical and Quantum Features of the Mixmaster Singularity

This review article is devoted to analyze the main properties characterizing the cosmological singularity associated to the homogeneous and inhomogeneous Mixmaster model. After the introduction of the main tools required to treat the cosmological issue, we review in details the main results got along the last forty years on the Mixmaster topic. We firstly assess the classical picture of the homogeneous chaotic cosmologies and, after a presentation of the canonical method for the quantization, we develop the quantum Mixmaster behavior. Finally, we extend both the classical and quantum features to the fully inhomogeneous case. Our survey analyzes the fundamental framework of the Mixmaster picture and completes it by accounting for recent and peculiar outstanding results.

gr-qc↗

arXiv2008

Parametrizing fluids in canonical quantum gravity

The problem of time is an unsolved issue of canonical General Relativity. A possible solution is the Brown-Kuchar mechanism which couples matter to the gravitational field and recovers a physical, i.e. non vanishing, observable Hamiltonian functional by manipulating the set of constraints. Two cases are analyzed. A generalized scalar fluid model provides an evolutionary picture, but only in a singular case. The Schutz' model provides an interesting singularity free result: the entropy per baryon enters the definition of the physical Hamiltonian. Moreover in the co-moving frame one is able to identify the time variable tau with the logarithm of entropy.

gr-qc↗

arXiv2008

Particles and fields within a unification scheme

We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. For instance, in a 5-dimensional Kaluza-Klein manifold we argue that the motion of charged spinning bodies is obtain in a Papapetrou-like formulation. As far as spinors are concerned, we outline how the gauge coupling can be recognized by a proper dependence on extra-coordinates and by the dimensional reduction procedure.

gr-qc↗

arXiv2008

On the Role of Viscosity in Early Cosmology

We present a discussion of the effects induced by bulk viscosity on the very early Universe stability. The viscosity coefficient is assumed to be related to the energy density $ρ$ via a power-law of the form $ζ=ζ_0 ρ^s$ (where $ζ_0, s=const.$) and the behavior of the density contrast in analyzed. In particular, we study both Einstein and hydrodynamic equations up to first and second order in time in the so-called quasi-isotropic collapsing picture near the cosmological singularity. As a result, we get a power-law solution existing only in correspondence to a restricted domain of $ζ_0$. The particular case of pure isotropic FRW dynamics is then analyzed and we show how the asymptotic approach to the initial singularity admits an unstable collapsing picture.

gr-qc↗

arXiv2008

Lorentz Gauge Theory and Spinor Interaction

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.

hep-th↗

arXiv2008

On the coupling between spinning particles and cosmological gravitational waves

The influence of spin in a system of classical particles on the propagation of gravitational waves is analyzed in the cosmological context of primordial thermal equilibrium. On a flat Friedmann-Robertson-Walker metric, when the precession is neglected, there is no contribution due to the spin to the distribution function of the particles. Adding a small tensor perturbation to the background metric, we study if a coupling between gravitational waves and spin exists that can modify the evolution of the distribution function, leading to new terms in the anisotropic stress, and then to a new source for gravitational waves. In the chosen gauge, the final result is that, in the absence of other kind of perturbations, there is no coupling between spin and gravitational waves.

gr-qc↗

arXiv2008

On Matter Coupling in 5D Kaluza-Klein Model

We analyze some unphysical features of the geodesic approach to matter coupling in a compactified Kaluza-Klein scenario, like the q/m puzzle and the huge massive modes. We propose a new approach, based on Papapetrou multipole expansion, that provides a new equation for the motion of a test particle. We show how this equation provides right couplings and does not generate huge massive modes.

gr-qc↗

arXiv2008

Quantum cosmology with a minimal length

Quantum cosmology in the presence of a fundamental minimal length is analyzed in the context of the flat isotropic and the Taub cosmological models. Such minimal scale comes out from a generalized uncertainty principle and the quantization is performed in the minisuperspace representation. Both the quantum Universes are singularity-free and (i) in the isotropic model no evidences for a Big-Bounce appear; (ii) in the Taub one a quasi-isotropic configuration for the Universe is predicted by the model.

gr-qc↗

arXiv2008

General Relativity as Classical Limit of Evolutionary Quantum Gravity

We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that a non-vanishing behavior of the Hamiltonian comes out. We then interpret such resulting non-zero ``energy'' of the gravitational field in terms of a dust fluid. This new matter contribution is co-moving to the slicing and it accounts for the ``materialization'' of a synchronous reference from the corresponding gauge condition. Further, we analyze the quantum dynamics of a generic inhomogeneous Universe as described by this evolutionary scheme, asymptotically to the singularity. We show how the phenomenology of such a model overlaps the corresponding Wheeler-DeWitt picture. Finally, we study the possibility of a Schrödinger dynamics of the gravitational field as a consequence of the correspondence inferred between the ensemble dynamics of stochastic systems and the WKB limit of their quantum evolution. We demonstrate that the time dependence of the ensemble distribution is associated with the first order correction in $\hbar$ to the WKB expansion of the energy spectrum.

gr-qc↗

arXiv2008

Cosmological implications of an evolutionary quantum gravity

The cosmological implications of an evolutionary quantum gravity are analyzed in the context of a generic inhomogeneous model. The Schrödinger problem is formulated and solved in the presence of a scalar field, an ultrarelativistic matter and a perfect gas regarded as the dust-clock. Considering the actual phenomenology, it is shown how the evolutionary approach overlaps the Wheeler-DeWitt one.

gr-qc↗

arXiv2008

Low-energy sector of 8-dimensional General Relativity: Electro-Weak model and neutrino mass

In a Kaluza-Klein space-time $V^{4}\otimes S^{3}$, we demonstrate that the dimensional reduction of spinors provides a 4-field, whose associated SU(2) gauge connections are geometrized. However, additional and gauge-violating terms arise, but they are highly suppressed by a factor $β$, which fixes the amount of the spinor dependence on extra-coordinates. The application of this framework to the Electro-Weak model is performed, thus giving a lower bound for $β$ from the request of the electric charge conservation. Moreover, we emphasize that also the Higgs sector can be reproduced, but neutrino masses are predicted and the fine-tuning on the Higgs parameters can be explained, too.

gr-qc↗

arXiv2007

Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework

The implications of a Generalized Uncertainty Principle on the Taub cosmological model are investigated. The model is studied in the ADM reduction of the dynamics and therefore a time variable is ruled out. Such a variable is quantized in a canonical way and the only physical degree of freedom of the system (related to the Universe anisotropy) is quantized by means of a modified Heisenberg algebra. The analysis is performed at both classical and quantum level. In particular, at quantum level, the motion of wave packets is investigated. The two main results obtained are as follows. i) The classical singularity is probabilistically suppressed. The Universe exhibits a stationary behavior and the probability amplitude is peaked in a determinate region. ii) The GUP wave packets provide the right behavior in the establishment of a quasi-isotropic configuration for the Universe.

gr-qc↗

arXiv2007

Macroscopic and Microscopic Paradigms for the Torsion Field: from the Test-Particle Motion to a Lorentz Gauge Theory

Torsion represents the most natural extension of General Relativity and it attracted interest over the years in view of its link with fundamental properties of particle motion. The bulk of the approaches concerning the torsion dynamics focus their attention on their geometrical nature and they are naturally led to formulate a non-propagating theory. Here we review two different paradigms to describe the role of the torsion field, as far as a propagating feature of the resulting dynamics is concerned. However, these two proposals deal with different pictures, i.e., a macroscopic approach, based on the construction of suitable potentials for the torsion field, and a microscopic approach, which relies on the identification of torsion with the gauge field associated with the local Lorentz symmetry. We analyze in some detail both points of view and their implications on the coupling between torsion and matter will be investigated. In particular, in the macroscopic case, we analyze the test-particle motion to fix the physical trajectory, while, in the microscopic approach, a natural coupling between torsion and the spin momentum of matter fields arises.

gr-qc↗

arXiv2007

Gravitational Stability and Bulk Cosmology

We present a discussion of the effects induced by bulk viscosity either on the very early Universe stability and on the dynamics associated to the extreme gravitational collapse of a gas cloud. In both cases the viscosity coefficient is related to the energy density $ρ$ via a power-law of the form $ζ=ζ_0 ρ^s$ (where $ζ_0, s=const.$) and the behavior of the density contrast in analyzed. In the first case, matter filling the isotropic and homogeneous background is described by an ultra-relativistic equation of state. The analytic expression of the density contrast shows that its growth is suppressed forward in time as soon as $ζ_0$ overcomes a critical value. On the other hand, in such a regime, the asymptotic approach to the initial singularity admits an unstable collapsing picture. In the second case, we investigate the top-down fragmentation process of an uniform and spherically symmetric gas cloud within the framework of a Newtonian approach, including the negative pressure contribution associated to the bulk viscous phenomenology. In the extreme regime toward the singularity, we show that the density contrast associated to an adiabatic-like behavior of the gas (which is identified by a particular range of the politropic index) acquire, for sufficiently large viscous contributions, a vanishing behavior which prevents the formation of sub-structures. Such a feature is not present in the isothermal-like collapse. We also emphasize that in the adiabatic-like case bulk viscosity is also responsible for the appearance of a threshold scale (equivalent to a Jeans length) beyond which perturbations begin to increase.

gr-qc↗

arXiv2007

Minisuperspace dynamics in a generalized uncertainty principle framework

The minisuperspace dynamics of the Friedmann-Robertson-Walker (FRW) and of the Taub Universes in the context of a Generalized Uncertainty Principle is analyzed in detail. In particular, the motion of the wave packets is investigated and, in both the models, the classical singularity appear to be probabilistic suppressed. Moreover, the FRW wave packets approach the Planckian region in a stationary way and no evidences for a Big-Bounce, as predicted in Loop Quantum Cosmology, appear. On the other hand, the Taub wave packets provide the right behavior in predicting an isotropic Universe.

gr-qc↗

arXiv2007

The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle

We analyze the quantum dynamics of the Friedmann-Robertson-Walker Universe in the context of a Generalized Uncertainty Principle. Since the isotropic Universe dynamics resembles that of a one-dimensional particle, we quantize it with the commutation relations associated to an extended formulation of the Heisenberg algebra. The evolution of the system is described in terms of a massless scalar field taken as a relational time. We construct suitable wave packets and analyze their dynamics from a quasi-classical region to the initial singularity. The appearance of a non singular dynamics comes out as far as the behavior of the probability density is investigated. Furthermore, reliable indications arise about the absence of a Big-Bounce, as predicted in recent issues of Loop Quantum Cosmology.

gr-qc↗

arXiv2007

Evolutionary Quantum Dynamics of a Generic Universe

The implications of an Evolutionary Quantum Gravity are addressed in view of formulating a new dark matter candidate. We consider a Schrödinger dynamics for the gravitational field associated to a generic cosmological model and then we solve the corresponding eigenvalues problem, inferring its phenomenological issue for the actual Universe. The spectrum of the super-Hamiltonian is determined including a free inflaton field, the ultrarelativistic thermal bath and a perfect gas into the dynamics. We show that, when a Planckian cut-off is imposed in the theory and the classical limit of the ground state is taken, then a dark matter contribution can not arise because its critical parameter $Ω_{dm}$ is negligible today when the appropriate cosmological implementation of the model is provided. Thus, we show that, from a phenomenological point of view, an Evolutionary Quantum Cosmology overlaps the Wheeler-DeWitt approach and therefore it can be inferred as appropriate to describe early stages of the Universe without significant traces on the later evolution. Finally, we provide indications that the horizon paradox can be solved in the Planck era by the morphology of the Universe wave function.

gr-qc↗

arXiv2007

Boost invariance of the gravitational field dynamics: quantization without time gauge

We perform a canonical quantization of gravity in a second-order formulation, taking as configuration variables those describing a 4-bein, not adapted to the space-time splitting. We outline how, neither if we fix the Lorentz frame before quantizing, nor if we perform no gauge fixing at all, is invariance under boost transformations affected by the quantization.

gr-qc↗