48 research outputs found
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
Mixmaster Chaos via the Invariant Measure
The chaoticity of the Mixmaster is discussed in the framework of Statistical
Mechanics by using Misner--Chitre-like variables and an ADM reduction of its
dynamics. We show that such a system is well described by a microcanonical
ensemble whose invariant measure is induced by the corresponding Liouville one
and is uniform. The covariance with respect to the choice of the temporal gauge
of the obtained invariant measure is outlined.Comment: 3 pages, 1 figure, proceedings of the X Marcel Grossmann Meeting
22-26 July, 2003, Rio de Janeir
Covariant Formulation of the Invariant Measure for the Mixmaster Dynamics
We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing
the covariant nature of its chaotic behavior with respect to any choice of time
variable. We construct the appropriate invariant measure for the system (which
relies on the existence of an ``energy-like'' constant of motion) without
fixing the time gauge, i.e. the corresponding lapse function. The key point in
our analysis consists of introducing generic Misner-Chitr\'e-like variables
containing an arbitrary function, whose specification allows one to set up the
same dynamical scheme in any time gauge.Comment: 11 pages, 1 figur