5,323 research outputs found
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
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 .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
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Camici bianchi e tute blu
Sul finire degli anni settanta, mentre le nostre facoltĂ universitarie vanno avvitandosi nella loro crisi, una parte del mondo accademico si rende conto dellâinadeguatezza di pratiche didattiche massificate e comincia a promuovere sporadiche iniziative di segno contrario: rapide, intense, ad alta densitĂ di interconnessione tra docenti e studenti. La necessitĂ 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 âsporcareâ positivamente le nostre autobiografie
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