413 research outputs found
Quantum Perfect-Fluid Kaluza-Klein Cosmology
The perfect fluid cosmology in the 1+d+D dimensional Kaluza-Klein spacetimes
for an arbitrary barotropic equation of state is quantized by using
the Schutz's variational formalism. We make efforts in the mathematics to solve
the problems in two cases. For the first case of the stiff fluid we
exactly solve the Wheeler-DeWitt equation when the space is flat. After the
superposition of the solutions we analyze the Bohmian trajectories of the
final-stage wave-packet functions and show that the flat spaces and the
compact spaces will eventually evolve into finite scale functions. For the
second case of , we use the approximated wavefunction in the
Wheeler-DeWitt equation to find the analytic forms of the final-stage
wave-packet functions. After analyzing the Bohmian trajectories we show that
the flat spaces will be expanding forever while the scale function of the
contracting spaces would not become zero within finite time. Our
investigations indicate that the quantum effect in the quantum perfect-fluid
cosmology could prevent the extra compact spaces in the Kaluza-Klein theory
from collapsing into a singularity or that the "crack-of-doom" singularity of
the extra compact dimensions is made to occur at .Comment: Latex 18 pages, add section 2 to introduce the quantization of
perfect flui
Troubles with quantum anistropic cosmological models: Loss of unitarity
The anisotropic Bianchi I cosmological model coupled with perfect fluid is
quantized in the minisuperspace. The perfect fluid is described by using the
Schutz formalism which allows to attribute dynamical degrees of freedom to
matter. A Schr\"odinger-type equation is obtained where the matter variables
play the role of time. However, the signature of the kinetic term is
hyperbolic. This Schr\"odinger-like equation is solved and a wave packet is
constructed. The norm of the resulting wave function comes out to be time
dependent, indicating the loss of unitarity in this model. The loss of
unitarity is due to the fact that the effective Hamiltonian is hermitian but
not self-adjoint. The expectation value and the bohmian trajectories are
evaluated leading to different cosmological scenarios, what is a consequence of
the absence of a unitary quantum structure. The consistency of this quantum
model is discussed as well as the generality of the absence of unitarity in
anisotropic quantum models.Comment: Latex file, 18 pages. To appear in General Relativity and Gravitatio
Dynamical Vacuum in Quantum Cosmology
By regarding the vacuum as a perfect fluid with equation of state p=-rho, de
Sitter's cosmological model is quantized. Our treatment differs from previous
ones in that it endows the vacuum with dynamical degrees of freedom. Instead of
being postulated from the start, the cosmological constant arises from the
degrees of freedom of the vacuum regarded as a dynamical entity, and a time
variable can be naturally introduced. Taking the scale factor as the sole
degree of freedom of the gravitational field, stationary and wave-packet
solutions to the Wheeler-DeWitt equation are found. It turns out that states of
the Universe with a definite value of the cosmological constant do not exist.
For the wave packets investigated, quantum effects are noticeable only for
small values of the scale factor, a classical regime being attained at
asymptotically large times.Comment: Latex, 19 pages, to appear in Gen. Rel. Gra
Quantum cosmological perfect fluid models
Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an
arbitrary barotropic equation of state are constructed using
Schutz's variational formalism. In this approach the notion of time can be
recovered. By superposition of stationary states, finite-norm wave-packet
solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale
factor is studied by applying the many-worlds and the ontological
interpretations of quantum mechanics. Singularity-free models are obtained for
.Comment: Latex file, 12 pages. New paragraphs in the Introduction and
Conclusion, and other minor corrections in the text and in some formulas.
Accepted for publication in General Relativity and Gravitatio
A Quantum Cosmological Model With Static and Dynamic Wormholes
Quantization is performed of a Friedmann-Robertson-Walker universe filled
with a conformally invariant scalar field and a perfect fluid with equation of
state . A well-known discrete set of static quantum wormholes is
shown to exist for radiation (), and a novel continuous set is
found for cosmic strings (), the latter states having throat
radii of any size. In both cases wave-packet solutions to the Wheeler-DeWitt
equation are obtained with all the properties of evolving quantum wormholes. In
the case of a radiation fluid, a detailed analysis of the quantum dynamics is
made in the context of the Bohm-de Broglie interpretation. It is shown that a
repulsive quantum force inversely proportional to the cube of the scale factor
prevents singularities in the quantum domain. For the states considered, there
are no particle horizons either.Comment: LaTex file, 13 pages. To appear in General Relativity and Gravitatio
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