Dynamics of Inhomogeneous Models Near a Singularity in Classical and Quantum Cosmology

Introduction: Generalized Kasner Variables in inhomogeneous cosmological - models Introduction Generalized Kasner model, Generalized Kasner Variables Generalized Kasner model Generalized Kasner variables The asymptotic model in the vicinity of a cosmological singularity - (the BLK model) Billiard reprsentation Misner-Chitre approach Properties of the Billiards Dynamics of inhomogeneities Estimates and Origin of cellular structure of space Quantum cosmology introduction local dynamics of inhomogeneous models Quantization. The Wheeler-De Witt equation The space of solutions to the WDW equation for a particular - x-set of degrees of freedom The Hilbert space and the probability interpretation The ambiguity in the choice of the Hilbert space The presence of matter and the case of all degree of freedom The presence of the scalar field. Mixing of frequencies and - third quantization The case of all degree of freedom The BLK inhomogeneous model, stationary states and statistical - properties of metric inhomogeneities Estimates and dynamical reduction of extra dimensions in Inhomogeneous - Kaluza-Klein cosmological models Third quantization and topology fluctuation in the early universe Introduction The Hamiltonian formulation Generalized Kazner solution and quantization Third quantization Interpretation and observables Topology fluctuations and quantum creation of a quasi-homogeneous - inflationary Universe On a Modification of the Ordinary Field Theory