Universität zu Köln

Kwidzinski, Nick (2020). Quantum Fate of Singularities in Anisotropic Cosmological Models. PhD thesis, Universität zu Köln.

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Abstract

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.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Kwidzinski, Nick nickkwidzinski1@gmail.com UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-116203
Date:	2020
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Quantum Gravity; Quantum Cosmology; Wheeler-DeWitt equation English
Date of oral exam:	30 June 2020
Referee:	Name Academic Title Kiefer, Claus Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/11620