Fingerprints of the Very Early Universe.
[Tesi di dottorato]
Tesi di dottorato
||Fingerprints of the Very Early Universe
|Number of Pages:
||Università degli Studi di Napoli Federico II
|Number of Pages:
||cosmologia, universo primordiale, big bang, mixmaster,
soluzione quasi-isotropa, inflation, quantum gravity
||Area 02 - Scienze fisiche > FIS/05 - Astronomia e astrofisica
||24 Oct 2005
||30 Apr 2014 19:22
During the work developed in the PhD Thesis, it has been faced a number of problems
concerning theoretical cosmology especially with respect dynamical evolution of the Universe
near the cosmological singularity.
Wide space has been devoted to the study of the subtle question concerning the covariance
chaoticity, which led to important issues favourable to the independence of the ‘’chaos’’ with
respect to the choice of the temporal gauge. Such analysis found its basis either on the
standard approach using the Jacobi metric (a scheme allowed by the existence of an energy
like constant of motion), either by a statistical mechanics approach in which the mixmaster
evolution is represented as a billiard on a Lobatchevski plane and therefore admitting a
microcanonical ensemble associated to such energy-like constant.
Furthermore, an important step consisted in searching a Physical link between the chaoticity
characterizing the system at a classical level and the quantum indeterminism appearing in the
Planckian era for such a model. More precisely it was constructed che canonical quantization of
the model via a Schroedinger approach (equivalent to the Wheeler-DeWitt scheme) and then
developed the WKB semiclassical limit to be compared with the classical dynamics. As an
issue, it resulted a correspondence between the continuity equation of the microcanonical
distribution function and that one describing the dynamics of the first order corrections in the
wave function for h 0.
It is remarkable the investigation performed about a quasi-isotropic inflationary solution, which
allowed to confirm how there is non chance for classical inhomogeneous perturbations to
survive after the DeSitter phase; such an analysis supports strongly the idea that only quantum
fluctuations ofthe scalar field can provide a satisfactory esplanation for the observed spectrum
of inhomogeneous perturbations.
A detailed discussion was pursued in view of clarifying the peculiarity existing to characterize
chaos in General Relativity; in particular, it has been provived a critical discussion on the
predictivity allowed by the fractal basin boundary approach in qualifying the nature of the
mixmaster dynamics; the main issue on this direction relies on the numerical approximations
limits when treating iterations of irrational numbers and overall on the potential methods
commonly adopted in the dynamical systems approach.
With this respect it is emphasized the ambiguity of describing chaos in terms of geodesic
deviation when the backgroun metric is a pseudo Riemannian one; a correct characterization of
the Lyapunov exponents required a projection of the connecting vector toward a Fermi basis.
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