arXiv subjects

Giovanni Montani

Publications and source records attributed to Giovanni Montani.

At least 91 records · Page 5Linked to original sources

arXiv2021

An Overview on the Nature of the Bounce in LQC and PQM

We present a review on basic aspects of quantum cosmology in the presence of cut-off physics. We first analyze how the Wheeler-DeWitt equation in a pure metric approach describes the quantum Universe, showing how the singularity is not removed. We then discuss basic features of loop quantum cosmology. For the isotropic Universe, we compare the original $μ_0$ scheme and the most commonly accepted formulation, the $\barμ$ scheme. Some results concerning the Bianchi Universes are also discussed. Finally, we consider some relevant criticisms on the real link between full loop quantum gravity and its minisuperspace implementation. In the second part of the review we consider the isotropic Universe and the Bianchi models in the framework of polymer quantum mechanics. We first address the polymerization in terms of the Ashtekar-Barbero-Immirzi connection and show how the resulting dynamics is isomorphic to the $μ_0$. Then we analyze the polymerization of volume-like variables, and we see the resulting dynamics is isomorphic to the $\barμ$ scheme with a fixed critical energy density. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model through a metric approach. We compare the results obtained by using the volume variable to the standard Misner variable. In the latter case we find a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations on changing variables in the polymer representation. In particular we consider how the dynamics can be mapped in two different sets of variables (at the price of using a coordinate-dependent lattice step), and we infer some possible implications on the equivalence of the $μ_0$ and $\barμ$ scheme of loop quantum cosmology.

gr-qc↗

arXiv2021

Quantum Dynamics of the Isotropic Universe in the Metric f(R) Gravity

We analyse the canonical quantum dynamics of the isotropic universe, as emerging from the Hamiltonian formulation of a metric f(R) gravity, viewed in the Jordan frame. The canonical method of quantization is performed by solving the Hamiltonian constraint before quantizing and adopting like a relational time the non-minimally coupled scalar field emerging in the Jordan frame. The resulting Schröedinger evolution is then investigated both in the vacuum and in the presence of a massless scalar field, though as the kinetic component of an inflaton. We show that, in vacuum, the morphology of localized wave packets is that of a non-spreading profile up to the cosmological singularity. When the external scalar field is included into the dynamics, we see that the wave packets acquire the surprising feature of increasing localization of the universe volume, as it expands. This result suggests that in the metric f(R) formulation of gravity, a spontaneous mechanism arises for the universe classicization. Actually, when the phase space of the scalar field is fully explored, such an increasing localization in the Universe volume is valid up to a given value of the time, i.e. of the non-minimally coupled mode after which the wave packets spread again. We conclude our analysis by inferring that before this critical transition age is reached, the inflationary phase could take place, here modelled via a cosmological constant. This point of view provides an interesting scenario for the transition from a Planckian Universe to a classical de-Sitter phase, which in the f(R) gravity appears more natural than in the Einsteinian picture.

gr-qc↗

arXiv2021

Axisymmetric Plasma Equilibria with Toroidal and Poloidal Velocity Fields: Tokamak Relevant Configurations

We analyze an axisymmetric equilibrium of a plasma endowed with toroidal and poloidal velocity fields, with the aim to characterize the influence of the global motion on the morphology of the magnetic confinement. We construct our configuration assuming that the poloidal velocity field is aligned with the poloidal magnetic field lines and, furthermore, we require that the plasma mass density depend on the magnetic flux function (or equivalently, that the plasma fluid be incompressible). We then derive a sort of Grad-Shafranov equation for such an equilibrium and implement it to tokamak relevant situations, with particular reference to TCV-like profiles. The main result of the present study concerns the emergence, in configurations associated to a double-null profile, of a closed surface of null pressure encorporating the two X-points of the magnetic configuration. This scenario suggests the possible existence of a new regime of the plasma equilibrium, corresponding to an improved plasma confinement near the X-points and a consequent reduced power transfer to the tokamak divertor.

physics.plasm-ph↗

arXiv2021

Influence of rotation on axisymmetric plasma equilibria: double-null DTT scenario

We study the dependence of some relevant tokamak equilibrium quantities on the toroidal plasma rotation. The Grad-Shafranov equation generalised to the rotating case is analytically solved employing two different representations for the homogenous solution. Using an expression in terms of polynomials, we describe the separatrix shape by a few geometrical parameters, reproducing different plasma scenarios such as double-null and inverse triangularity. In this setting, the introduction of toroidal rotation corresponds to variations on relevant plasma quantities, most notably an enhancement of the poloidal beta. Using a more general expression in terms of Bessel functions, we reconstruct the full plasma boundary of the double-null configuration proposed for the upcoming DTT experiment, demonstrating how said configuration is compatible with different values of the plasma velocity.

physics.plasm-ph↗

arXiv2021

On the Hubble constant tension in the SNe Ia Pantheon sample

The Hubble constant ($H_0$) tension between Type Ia Supernovae (SNe Ia) and Planck measurements ranges from 4 to 6 $σ$. To investigate this tension, we estimate $H_{0}$ in the $Λ$CDM and $w_{0}w_{a}$CDM models by dividing the Pantheon sample, the largest compilation of SNe Ia, into 3, 4, 20 and 40 bins. We fit the extracted $H_{0}$ values with a function mimicking the redshift evolution: $g(z)={H_0}(z)=\tilde{H}_0/(1+z)^α$, where $α$ indicates an evolutionary parameter and $\tilde{H}_0=H_0$ at $z=0$. We set the absolute magnitude of SNe Ia so that $H_0=73.5\,\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$, and we fix fiducial values for $Ω_{0m}^{ΛCDM}=0.298$ and $Ω_{0m}^{w_{0}w_{a}CDM}=0.308$. We find that $H_0$ evolves with redshift, showing a slowly decreasing trend, with $α$ coefficients consistent with zero only from 1.2 to 2.0 $σ$. Although the $α$ coefficients are compatible with 0 in 3 $σ$, this however may affect cosmological results. We measure locally a variation of $H_0(z=0)-H_0(z=1)=0.4\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$ in 3 and 4 bins. Extrapolating ${H_0}(z)$ to $z=1100$, the redshift of the last scattering surface, we obtain values of $H_0$ compatible in 1 $σ$ with Planck measurements independently of cosmological models and number of bins we investigated. Thus, we have reduced the $H_0$ tension from $54\%$ to $72\%$ for the $Λ$CDM and $w_{0}w_{a}$CDM models, respectively. If the decreasing trend of $H_0(z)$ is real, it could be due to astrophysical selection effects or to modified gravity.

astro-ph.CO↗

arXiv2021

Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case

We extend the notion of the Nieh-Yan invariant to generic metric-affine geometries, where both torsion and nonmetricity are taken into account. Notably, we show that the properties of projective invariance and topologicity can be independently accommodated by a suitable choice of the parameters featuring this new Nieh-Yan term. We then consider a special class of modified theories of gravity able to promote the Immirzi parameter to a dynamical scalar field coupled to the Nieh-Yan form, and we discuss in more detail the dynamics of the effective scalar tensor theory stemming from such a revised theoretical framework. We focus, in particular, on cosmological Bianchi I models and we derive classical solutions where the initial singularity is safely removed in favor of a big-bounce, which is ultimately driven by the non-minimal coupling with the Immirzi field. These solutions, moreover, turn out to be characterized by finite time singularities, but we show that such critical points do not spoil the geodesic completeness and wave regularity of these space-times.

gr-qc↗

arXiv2021

Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation

The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical approach to the problem of time, that has the main goal of reproducing quantum field theory on a fixed WKB background accounting also for quantum gravity corrections. We analyze the different choices of the expansion parameter and discuss the problems arising in previous proposals, where a non-unitary evolution emerges as an effect of quantum gravity corrections. In this work we develop a new approach to solve this problem by performing the WKB expansion with the introduction of the so-called kinematical action as a clock for quantum matter, that allows to recover a unitary dynamics.

gr-qc↗

arXiv2021

Kaluza-Klein theories in the framework of Polymer Quantum Mechanics

We provide a re-analysis of the $5D$ Kaluza-Klein theory by implementing the polymer representation of the dynamics, both on a classical and a quantum level, in order to introduce in the model information about the existence of a cut-off scale. We start by showing that, in the framework of semi-classical quantum mechanics, the $5D$ Bianchi I model admits a solution in which three space directions expand isotropically, while the remaining one is static, offering in this way a very valuable scenario to implement a Kaluza-Klein paradigm, identifying in such a static dimension the compactified one. We then analyse the behaviour of geodesic motion in the context of the polymer representation, as referred to a $5D$ space-time with a static dimension. We demonstrate that such a revised formulation allows overcoming one of the puzzling questions of the standard Kaluza-Klein model corresponding to the limit of the charge to mass ratio for a particle, inapplicable to any fundamental one. Indeed, here, such a ratio can be naturally attributed to particles predicted by the Standard Model and no internal contradiction of the theory arises on this level. Finally, we study the morphology of the field equation associated with a charged scalar particle, i.e. we analyse a Klein-Gordon equation, which fifth coordinate is viewed in the polymer representation. Here we obtain the surprising result that, although the Kaluza-Klein tower has a deformed structure characterized by irregular steps, the value predicted for the particle mass can be, in principle, set within the Standard Model mass distribution and hence, the problem of the Planckian value of such mass, typical of the standard formulation, is now overcome. However, a problem with the charge to mass ratio still survives in this quantum field formulation.

gr-qc↗

arXiv2021

A Scenario for a Singularity-free Generic Cosmological Solution

We develop a scenario for the emergence of a non-singular generic cosmological solution based on the a WKB characterization of one of the two anisotropy degrees of freedom. We investigate the dynamics of the so-called inhomogeneous mixmaster in the "corner" configuration and inferring that one of the two anisotropic variables becomes small enough to explore the uncertainty principle. Then, we apply a standard WKB approximation to the dynamics of the Universe which has macroscopic volume, one macroscopic anisotropy and one microscopic quantum degree of freedom. Our study demonstrates the possibility that the Universe acquires a non-singular classical behavior, retaining the quantum degree of freedom as a small oscillating ripple on a stationary Universe. The role of the so-called "fragmentation process" is also taken into account in outlining the generality of such a behavior in independent local space regions.

gr-qc↗

arXiv2021

Features of the Primordial Universe in f(R)-gravity as viewed in the Jordan frame

We analyze some relevant features of the primordial Universe as viewed in the Jordan frame formulation of the f(R)-gravity, especially when the potential term of the non-minimally coupled scalar field is negligible. We start formulating the Hamiltonian picture in the Jordan frame, using the 3-metric determinant as a basic variable and we outline that its conjugated momentum appears linearly only in the scalar constraint. Then, we construct the basic formalism to characterize the dynamics of a generic inhomogeneous cosmological model and specialize it in order to describe behaviors of the Bianchi Universes, both on a classical and a quantum regime. As a fundamental issue, we demonstrate that, when the potential term of the additional scalar mode is negligible near enough to the initial singularity, the Bianchi IX cosmology is no longer affected by the chaotic behavior, typical in vacuum of the standard Einsteinian dynamics. In fact, the presence of stable Kasner stability region and its actractive character are properly characterized. Finally, we investigate the canonical quantization of the Bianchi I model, using as time variable the non-minimally coupled scalar field and showing that the existence of a conserved current is outlined for the corresponding Wheeler-DeWitt equation. The behavior of a localized wave-packet for the isotropic Universe is also evolved, demonstrating that the singularity is still present in this revised quantum dynamics.

gr-qc↗

arXiv2021

Super-entropic black hole with Immirzi hair

In the context of f(R) generalizations to the Holst action, endowed with a dynamical Immirzi field, we derive an analytic solution describing asymptotically Anti-de Sitter black holes with hyperbolic horizon. These exhibit a scalar hair of the second kind, which ultimately depends on the Immirzi field radial behaviour. In particular, we show how the Immirzi field modifies the usual entropy law associated to the black hole. We also verify that the Immirzi field boils down to a constant value in the asymptotic region, thus restoring the standard Loop Quantum Gravity picture. We finally prove the violation of the reverse isoperimetric inequality, resulting in the super-entropic nature of the black hole, and we discuss in detail the thermodynamic stability of the solution.

gr-qc↗

arXiv2021

General features of the linear crystalline morphology of accretion disks

In this paper, we analyze the so-called Master Equation of the linear backreaction of a plasma disk in the central object magnetic field, when small scale ripples are considered. This study allows to single out two relevant physical properties of the linear disk backreaction: (i) the appearance of a vertical growth of the magnetic flux perturbations; (ii) the emergence of sequence of magnetic field O-points, crucial for the triggering of local plasma instabilities. We first analyze a general Fourier approach to the solution of the addressed linear partial differential problem. This technique allows to show how the vertical gradient of the backreaction is, in general, inverted with respect to the background one. Instead, the fundamental harmonic solution constitutes a specific exception for which the background and the perturbed profiles are both decaying. Then, we study the linear partial differential system from the point of view of a general variable separation method. The obtained profile describes the crystalline behavior of the disk. Using a simple rescaling, the governing equation is reduced to the second order differential Whittaker equation. The zeros of the radial magnetic field are found by using the solution written in terms Kummer functions. The possible implications of the obtained morphology of the disk magnetic profile are then discussed in view of the jet formation.

astro-ph.HE↗

arXiv2020

Gravitational Landau Damping for massive scalar modes

We establish the possibility of Landau damping for gravitational scalar waves which propagate in a non-collisional gas of particles. In particular, under the hypothesis of homogeneity and isotropy, we describe the medium at the equilibrium with a Jüttner-Maxwell distribution, and we analytically determine the damping rate from the Vlasov equation. We find that damping occurs only if the phase velocity of the wave is subluminal throughout the propagation within the medium. Finally, we investigate relativistic media in cosmological settings by adopting numerical techniques.

gr-qc↗

arXiv2020

Generalized Ashtekar variables for Palatini f(R) models

We consider special classes of Palatini f(R) theories, featured by additional Loop Quantum Gravity inspired terms, with the aim of identifying a set of modified Ashtekar canonical variables, which still preserve the SU(2) gauge structure of the standard theory. In particular, we allow for affine connection to be endowed with torsion, which turns out to depend on the additional scalar degree affecting Palatini f(R) gravity, and in this respect we successfully construct a novel Gauss constraint. We analyze the role of the additional scalar field, outlining as it acquires a dynamical character by virtue of a non vanishing Immirzi parameter, and we describe some possible effects on the area operator stemming from such a revised theoretical framework. Finally, we compare our results with earlier studies in literature, discussing differences between metric and Palatini approaches. It is worth noting how the Hamiltonian turns out to be different in the two cases. The results can be reconciled when the analysis is performed in the Einstein frame.

gr-qc↗

arXiv2020

Contributions to the linear and non-linear theory of the beam-plasma interaction

We focus our attention on some relevant aspects of the beam-plasma instability in order to refine some features of the linear and non-linear dynamics. After a re-analysis of the Poisson equation and of the assumption dealing with the background plasma in the form of a linear dielectric, we study the non-perturbative properties of the linear dispersion relation, showing the necessity for a better characterization of the mode growth rate in those flat regions of the distribution function where the Landau formula is no longer predictive. We then upgrade the original N-body approach, in order to include a return current in the background plasma. This correction term is responsible for smaller saturation levels and growth rates of the Langmuir modes, as result of the energy density transferred to the plasma via the return current. Finally, we include friction effects, as those due to the collective influence of all the plasma charges on the motion of the beam particles. The resulting force induces a progressive resonance detuning, because particles are losing energy and decreasing their velocity. This friction phenomenon gives rise to a deformation of the distribution function, associated with a significant growth of the less energetic particle population. The merit of this work is to show how a fine analysis of the beam-plasma instability outlines a number of subtleties about the linear, intermediate and late dynamics which can be of relevance when such a system is addressed as a paradigm to describe relevant nonlinear wave-particle phenomena.

physics.plasm-ph↗

arXiv2020

Resonance overlap and non-linear features of the beam-plasma system

The beam-plasma instability can be addressed as a reduced model in several contexts of plasma physics, from space to fusion plasma. In this paper, we review and refine some non-linear features of this model. Specifically, by analyzing the dependence of the non-linear velocity spread as a function of the linear growth rate, we discuss the effective size of the resonance in view of its role in the spectral overlap at saturation. The relevance of this characterization relies on the necessity of a quantitative determination of the overlap degree to discriminate among different transport regimes of the self consistent dynamics. The analysis is enriched with a study of the phase-space dynamics by means of the Lagrangian Coherent Structure technique, in order to define the transport barriers of the system describing the relevant features of the overlap process. Finally, we discuss relevant features related to the mode saturation levels.

physics.plasm-ph↗

arXiv2020

Dynamics of quantum anisotropies in a Taub Universe in the WKB approximation

We analyze the dynamics of a Taub cosmological model in the presence of a massless minimally coupled scalar field and a cosmological constant, in the limit when both the Universe volume and the scalar field live in a quasi-classical approximation. By other words, we study the dynamics of a quantum small anisotropy evolving on a de Sitter background and in the presence of a kinetic term of the inflaton field. We demonstrate that the quantum anisotropy exponentially decays during the Universe expansion, approaching a finite and small value. This result suggests that the quantum isotropization of the Universe during a de Sitter phase is much weaker than the corresponding classical evolution, favouring the survival of certain degree of anisotropy to the de Sitter phase. Finally we analyze the case when also the scalar field is considered as quantum variable, by showing how its variance naturally spreads because of no potential term significantly affects its dynamics. This behaviour results to be different from the anisotropy which is subjected to the potential coming out from the spatial curvature.

gr-qc↗

arXiv2020

WKB Approximation for the Polymer Quantization of the Taub Model

We develop a suitable technical algorithm to implement a separation of the Minisuperspace configurational variables into quasi-classical and purely quantum degrees of freedom, in the framework of a Polymer quantum Mechanics reformulation of the canonical dynamics. We then implement the obtained general scheme to the specific case of a Taub Universe, in the presence of a free massless scalar field. In particular, we identify the quasi-classical variables in the Universe volume and a suitable function of the scalar field, while the purely quantum degree of freedom corresponds to the Universe anisotropy. We demonstrate that the Taub cosmology is associated to a cyclical Universe, oscillating between a minimum and maximum volume turning points, respectively. The pure quantum Universe anisotropy has always a finite value.

gr-qc↗