Erçetin, Utku (2024) Computing CMB Anisotropies in Compact Hyperbolic Universes. Bachelor's Thesis, Mathematics.
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Abstract
The topology of the universe remains a fundamental question in cosmology, with com- pact hyperbolic 3-manifolds offering a compelling framework to explain anomalies in the cosmic microwave background (CMB) anisotropies. This thesis investigates the vibra- tional eigenmodes of such manifolds by solving the Laplace-Beltrami eigenvalue problem, (∆ + q2)Ψ = 0. Using the ‘method of ghosts,’ we attempt to numerically construct eigen- functions on the universal cover H3, ensuring invariance under the isometry group Γ, which acts freely and discontinuously on H3 to yield the compact space M/Γ. Despite a meticulous implementation of the methodology outlined in [1], we were unable to replicate the reported numerical results for eigenvalues and their multiplicities. Our findings sug- gest the need for further refinement and validation of these methods to establish a robust computational framework for investigating compact hyperbolic manifolds.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Seri, M. and Meerburg, P.D. and Scholtens, R.W. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 17 Dec 2024 10:34 |
| Last Modified: | 17 Dec 2024 10:34 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/34499 |
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