Semi-Classical Isotropization of the Universe during a de Sitter phase

Semi-classical states for the Wheeler-DeWitt equation of a Bianchi type I model in the presence of a scalar field are analyzed. It is outlined how this scheme can effectively describe more general situations, where the curvature of the Bianchi type IX model and a proper potential term for the scalar field are present. The introduction of a cosmological constant term accounts for the quasi-isotropization mechanism which bridges the proposed framework with a late isotropic phase. This result makes the semi-classical Bianchi I model a plausible scenario for the Universe pre-inflationary phase.Comment: 6 pages, accepted for publication in Phys. Rev.

Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable

We analyze the semiclassical and quantum behavior of the Bianchi IX Universe in the Polymer Quantum Mechanics framework, applied to the isotropic Misner variable, linked to the space volume of the model. The study is performed both in the Hamiltonian and field equations approaches, leading to the surprising result of a still singular and chaotic cosmology, whose Poincar\'e return map asymptotically overlaps the standard Belinskii-Khalatnikov-Lifshitz one. In the quantum sector, we reproduce the original analysis due to Misner, within the revised Polymer approach and we arrive to demonstrate that the quantum numbers of the point-Universe still remain constants of motion. This issue confirms the possibility to have quasi-classical states up to the initial singularity. The present study clearly demonstrates that the asymptotic behavior of the Bianchi IX Universe towards the singularity is not significantly affected by the Polymer reformulation of the spatial volume dynamics both on a pure quantum and a semiclassical level.Comment: 25 pages, 10 figures. v2: more discussions/clarification adde

Classical and quantum behavior of the generic cosmological solution

In the present paper we generalize the original work of C.W. Misner \cite{M69q} about the quantum dynamics of the Bianchi type IX geometry near the cosmological singularity. We extend the analysis to the generic inhomogeneous universe by solving the super-momentum constraint and outlining the dynamical decoupling of spatial points. Firstly, we discuss the classical evolution of the model in terms of the Hamilton-Jacobi approach as applied to the super-momentum and super-Hamiltonian constraints; then we quantize it in the approximation of a square potential well after an ADM reduction of the dynamics with respect to the super-momentum constraint only. Such a reduction relies on a suitable form for the generic three-metric tensor which allows the use of its three functions as the new spatial coordinates. We get a functional representation of the quantum dynamics which is equivalent to the Misner-like one when extended point by point, since the Hilbert space factorizes into $\infty^3$ independent components due to the parametric role that the three-coordinates assume in the asymptotic potential term. Finally, we discuss the conditions for having a semiclassical behavior of the dynamics and we recognize that this already corresponds to having mean occupation numbers of order $\mathcal{O}(10^2)$.Comment: 8 pages, AIP Proceedings, Eistein Century Conference, Paris 200

General Aspects of the de Sitter phase

We present a detailed discussion of the inflationary scenario in the context of inhomogeneous cosmologies. After a review of the fundamental features characterizing the inflationary model, as referred to a homogeneous and isotropic Universe, we develop a generalization in view of including small inhomogeneous corrections in the theory. A second step in our discussion is devoted to show that the inflationary scenario provides a valuable dynamical ``bridge'' between a generic Kasner-like regime and a homogeneous and isotropic Universe in the horizon scale. This result is achieved by solving the Hamilton-Jacobi equation for a Bianchi IX model in the presence of a cosmological space-dependent term. In this respect, we construct a quasi-isotropic inflationary solution based on the expansion of the Einstein equations up to first-two orders of approximation, in which the isotropy of the Universe is due to the dominance of the scalar field kinetic term; the first order of approximation corresponds to the inhomogeneous corrections and is driven by the matter evolution. We show how such a quasi-isotropic solution contains a certain freedom in fixing the space functions involved in the problem. The main physical issue of this analysis corresponds to outline the impossibility for the classical origin of density perturbations, due to the exponential decay of the matter term during the de Sitter phase.Comment: 30 pages with cimento.cls, no figures, to appear on "Il Nuovo Cimento B

Camici bianchi e tute blu

Sul finire degli anni settanta, mentre le nostre facoltà universitarie vanno avvitandosi nella loro crisi, una parte del mondo accademico si rende conto dell’inadeguatezza di pratiche didattiche massificate e comincia a promuovere sporadiche iniziative di segno contrario: rapide, intense, ad alta densità di interconnessione tra docenti e studenti. La necessità di interpretare situazioni complesse rispondendo a diversi interlocutori ha di fatto stimolato una interessante e variegata produzione progettuale, nella quale tutti noi, tolto il camice bianco e indossata la tuta blu, abbiamo trovato il modo di immergerci nella sperimentazione e “sporcare” positivamente le nostre autobiografie