Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

Abstract

Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D_m* and the lens spaces L(p,1).

v3. Final published version. 27 pages, 1 figure

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Cited by in corpus (7)

• Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
• Three-qubit entangled embeddings of CPT and Dirac groups within E8 Weyl group
• On the geometry and invariants of qubits, quartits and octits
• Cosmic topology. Part IIIa. Microwave background parity violation without parity-violating microphysics
• CMB radiation in an inhomogeneous spherical space
• How well-proportioned are lens and prism spaces?
• Orbifold construction of the modes of the Poincare dodecahedral space