Duff, Ramsay (2021) Conservation of Energy in de Sitter Space. Bachelor's Thesis, Physics.
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Abstract
The Universe appears to have a positive Cosmological Constant. If spacetime is curved, with de Sitter space being a good approximation, then since for every continuous isometry there is a cor- responding conserved Noether Current, there are implications for the conservation of energy due to the fact that the de Sitter and Poincaré Lie Groups differ. This project does three things; first, it shows how as the de Sitter radius approaches infinity, the de Sitter Lie Group approaches becoming the Poincaré Group of the isometries of flat Minkowski space under ̇Inönü Wigner Contraction. Secondly, this project finds the Noether currents corresponding to the Poincaré and de Sitter Groups’ Generators to compare the conservation laws of Minkowski and de Sitter space, showing that while the isometry group of Minkowski space has corresponding conservation laws which include global conservation of energy, the same is not the case for de Sitter space (unless the de Sitter radius approaches infinity). Finally, it is shown that when dealing with static patch coordinates, one can have a Killing vector which is timelike, therefore giving rise to energy conservation, within the horizon of the static patch, although not globally (however since the distance of the horizon is inversely proportional to the Cosmological Constant, which empirical research suggests is tiny, the patch is extremely large). With this taken into account, the results are discussed with suggestions for future research.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Boer, D. |
| Degree programme: | Physics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 13 Jul 2021 13:57 |
| Last Modified: | 30 May 2022 11:55 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/25147 |
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