The problem of time in quantum cosmology
This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations of minisuperspace models. In the second part, we focus on a specific minisupers...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2023
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| Online Access: | https://eprints.nottingham.ac.uk/71867/ |
| _version_ | 1848800698084360192 |
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| author | Menéndez-Pidal de Cristina, Lucía |
| author_facet | Menéndez-Pidal de Cristina, Lucía |
| author_sort | Menéndez-Pidal de Cristina, Lucía |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations of minisuperspace models. In the second part, we focus on a specific minisuperspace universe, analyse it classically, and quantise it using the canonical quantisation method. The chosen model is a flat FLRW universe with a free massless scalar field and a perfect fluid. We explain how different types of perfect fluid can be accommodated in our model. We extract the Wheeler–DeWitt equation, and calculate its solutions. There are three dynamical variables that may be used as clock parameters, namely a coordinate t conjugated to the perfect fluid mass, the massless scalar field φ, and v, a positive power of the scale factor. We define three quantum theories, each one based on assuming one of the previous dynamical quantities as the clock. This quantisation method is then compared with the Dirac quantisation. We find that, in each quantisation procedure, covariance is broken, leading to inequivalent quantum theories. In the third part, the properties of each theory are analysed. Unitarity of each theory is implemented by adding a boundary condition on the allowed states. The solutions to the boundary conditions are calculated and their properties are listed. Requiring unitarity is what breaks general covariance in the quantum theory. In the fourth part, we study the numerical properties of the wave functions in the three theories, paying special attention to singularity resolution and other divergences from the classical theory. The t-clock theory is able to resolve the singularity, the φ-clock theory presents some non trivial dynamics that can be associated with a resolution of spatial infinity, and the v-clock theory does not show significant deviations from the classical theory. In the last part, we expand our analysis in order to include another quantisation method: path integralquantisation, and finally, we conclude. |
| first_indexed | 2025-11-14T20:55:41Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-71867 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:55:41Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-718672023-07-26T04:40:04Z https://eprints.nottingham.ac.uk/71867/ The problem of time in quantum cosmology Menéndez-Pidal de Cristina, Lucía This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations of minisuperspace models. In the second part, we focus on a specific minisuperspace universe, analyse it classically, and quantise it using the canonical quantisation method. The chosen model is a flat FLRW universe with a free massless scalar field and a perfect fluid. We explain how different types of perfect fluid can be accommodated in our model. We extract the Wheeler–DeWitt equation, and calculate its solutions. There are three dynamical variables that may be used as clock parameters, namely a coordinate t conjugated to the perfect fluid mass, the massless scalar field φ, and v, a positive power of the scale factor. We define three quantum theories, each one based on assuming one of the previous dynamical quantities as the clock. This quantisation method is then compared with the Dirac quantisation. We find that, in each quantisation procedure, covariance is broken, leading to inequivalent quantum theories. In the third part, the properties of each theory are analysed. Unitarity of each theory is implemented by adding a boundary condition on the allowed states. The solutions to the boundary conditions are calculated and their properties are listed. Requiring unitarity is what breaks general covariance in the quantum theory. In the fourth part, we study the numerical properties of the wave functions in the three theories, paying special attention to singularity resolution and other divergences from the classical theory. The t-clock theory is able to resolve the singularity, the φ-clock theory presents some non trivial dynamics that can be associated with a resolution of spatial infinity, and the v-clock theory does not show significant deviations from the classical theory. In the last part, we expand our analysis in order to include another quantisation method: path integralquantisation, and finally, we conclude. 2023-07-26 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/71867/1/thesis.pdf Menéndez-Pidal de Cristina, Lucía (2023) The problem of time in quantum cosmology. PhD thesis, University of Nottingham. quantum gravity quantum cosmology problem of time singularity resolution |
| spellingShingle | quantum gravity quantum cosmology problem of time singularity resolution Menéndez-Pidal de Cristina, Lucía The problem of time in quantum cosmology |
| title | The problem of time in quantum cosmology |
| title_full | The problem of time in quantum cosmology |
| title_fullStr | The problem of time in quantum cosmology |
| title_full_unstemmed | The problem of time in quantum cosmology |
| title_short | The problem of time in quantum cosmology |
| title_sort | problem of time in quantum cosmology |
| topic | quantum gravity quantum cosmology problem of time singularity resolution |
| url | https://eprints.nottingham.ac.uk/71867/ |