Computational modeling demonstrates Gaussian pseudo-random expansion coefficients in a compact hyperbolic space, highlighting methods to evaluate cosmic microwave background anisotropy.
Measurements of CMB anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected(MC) compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. We numerically obtain the low-lying eigenmodes on a compact 3-hyperbolic space called m003(-2,3) in the SnapPea using the direct boundary element method. The computed eigenmodes are expanded in terms of eigenmodes on the unit three- dimensional pseudosphere. We numerically find that the expansion coefficients behave as gaussian pseudo-random numbers for low-lying eigenmodes.
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Kaiki Taro Inoue (1999) studied this question.
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