Eigenmodes of 3-dimensional spherical spaces and their application to cosmology

Details Eigenmodes of 3-dimensional spherical spaces and their application to cosmology Eigenmodes of 3-dimensional spherical spaces and their application to cosmology

2002-05-02

arxiv.org/abs/gr-qc/0205009v1

Class.Quant.Grav. 19 (2002) 4683-4708

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages, 24 figures

Scientific paper

10.1088/0264-9381/19/18/305

This article investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular, whereas in the Euclidean case too small universes are excluded by present CMB data, in the spherical case there will always exist candidate topologies even if the total energy density parameter of the universe is very close to unity.

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