13 research outputs found
Quantum Fate of Singularities in Anisotropic Cosmological Models
This thesis studies the possibility of the quantum avoidance of gravitational singularities in
anisotropic cosmological models.
For that purpose, we review the fundamentals of spatially homogeneous cosmological
models and quantum cosmology based on the Wheeler-DeWitt equation in minisuperspace.
Furthermore, we introduce a generalized dynamical system which is designed to emulate some
of the main features of the cosmological models. After studying its geometric properties, we
start to investigate how one can approach the canonical quantization of such a system. The
main focus of our analysis is on the factor ordering problem in the Wheeler-DeWitt equation.
The considerations motivate us to formulate criteria for singularity avoidance, that respect
the conformal geometry of the con�guration space of the spatially homogeneous models.
We then go on by studying some speci�c models with and without matter. In particular
we examine classical and quantum properties of the Bianchi type I, II and IX and the
Kantowski-Sachs universe. The criteria we developed previously are applied to see under
which circumstances singularities can be avoided. If the potential terms are negligible when
compared against the velocity terms in the gravitational action, the approach towards the
singularity is called asymptotically velocity term dominated. We �nd that such singularities
can be resolved, if the dimension of the minisuperspace is suffciently large. The underlying
mechanism is a spreading of wave packets in minisuperspace.
We also consider the non-diagonal Bianchi IX model with tilted dust. This model is
relevant in the context of the BKL scenario. We pay particular attention to the asymptotic
regime close to the singularity and the temporal behavior of curvature invariants in this
regime
On the dynamics of the general Bianchi IX spacetime near the singularity
We show that the complex dynamics of the general Bianchi IX universe in the
vicinity of the spacelike singularity can be approximated by a simplified
system of equations. Our analysis is mainly based on numerical simulations. The
properties of the solution space can be studied by using this simplified
dynamics. Our results will be useful for the quantization of the general
Bianchi IX model.Comment: 20 pages, 5 figures, minor change
Comparing the dynamics of diagonal and general Bianchi IX spacetime
We make comparison of the dynamics of the diagonal and nondiagonal Bianchi IX
models in the evolution towards the cosmological singularity. Apart from the
original variables, we use the Hubble normalized ones commonly applied in the
examination of the dynamics of homogeneous models. Applying the dynamical
systems method leads to the result that in both cases the continuous space of
critical points is higher dimensional and they are of the nonhyperbolic type.
This is a generic feature of the dynamics of both cases and seems to be
independent on the choice of phase space variables. The topologies of the
corresponding critical spaces are quite different. We conjecture that the
nondiagonal case may carry a new type of chaos different from the one specific
to the usually examined diagonal one.Comment: 25 pages, 2 figures, version including numerical simulations of
dynamic
Classical and quantum cosmology of Born-Infeld type models
We discuss Born-Infeld type fields (tachyon fields) in classical and quantum
cosmology. We first partly review and partly extend the discussion of the
classical solutions and focus in particular on the occurrence of singularities.
For quantization, we employ geometrodynamics. In the case of constant
potential, we discuss both Wheeler-DeWitt quantization and reduced
quantization. We are able to give various solutions and discuss their
asymptotics. For the case of general potential, we transform the Wheeler-DeWitt
equation to a form where it leads to a difference equation. Such a difference
equation was previously found in the quantization of black holes. We give
explicit results for the cases of constant potential and inverse squared
potential and point out special features possessed by solutions of the
difference equation.Comment: 14 pages, 8 figures, published versio
Curvature invariants for the Bianchi IX spacetime filled with tilted dust
We present an analysis of the Kretschmann and Weyl squared scalars for the general Bianchi IX model filled with tilted dust. Particular attention is given to the asymptotic regime close to the singularity for which we provide heuristic considerations supported by numerical simulations. The present paper is an extension of our earlier publication (Kiefer et al., in Eur Phys J C 78:691, 2018)
Singularity avoidance in anisotropic quantum cosmology
We discuss the fate of the classical singularities in quantum cosmological models. We state our
criteria of singularity avoidance and apply them to Friedmann-Lemaˆıtre models models as well as, in more
detail, to the anisotropic case of a Bianchi I universe. We find that the classical singularities are generally
avoided in these cases
Singularity avoidance in Bianchi I quantum cosmology
We extend recent discussions of singularity avoidance in quantum gravity from
isotropic to anisotropic cosmological models. The investigation is done in the
framework of quantum geometrodynamics (Wheeler-DeWitt equation). We formulate
criteria of singularity avoidance for general Bianchi class A models and give
explicit and detailed results for Bianchi I models with and without matter. We
find that the classical singularities can generally be avoided in these models.Comment: 15 pages, 8 figures, final versio
Hamiltonian formulation of dust cloud collapse
We consider the gravitational collapse of a self-gravitating spherical dust cloud in the Hamiltonian formalism. We address both homogeneous and inhomogeneous cases. Our novel derivation of the Hamiltonian of the system is based on an improved variational principle. It differs from usual treatments due to the presence of an extra boundary term added to the Hilbert action. As expected, the standard equations of motion are retrieved. However, differently from other treatments, the total Hamiltonian obtained with our procedure in the Schwarzschild time gauge is identical to the total mass of the system as measured from infinity, as it would be expected. Implications for the quantization of the system arc suggested