Computation of eigenmodes on a compact hyperbolic 3-space

Details Computation of eigenmodes on a compact hyperbolic 3-space Computation of eigenmodes on a compact hyperbolic 3-space

1998-10-02

arxiv.org/abs/astro-ph/9810034v3

Class.Quant.Grav. 16 (1999) 3071-3094

Astronomy and Astrophysics

Astrophysics

40 pages, 8 EPS figures; error estimation is included; accepted Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/16/10/304

Measurements of cosmic microwave background (CMB) anisotropy are ideal experiments for discovering the non-trivial global topology of the universe. To evaluate the CMB anisotropy in multiply-connected compact cosmological models, one needs to compute the eigenmodes of the Laplace-Beltrami operator. Using the direct boundary element method, we numerically obtain the low-lying eigenmodes on a compact hyperbolic 3-space called the Thurston manifold which is the second smallest in the known compact hyperbolic 3-manifolds. 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. The observed gaussianity in the CMB fluctuations can partially be attributed to the Gaussian pseudo-randomness of the expansion coefficients assuming that the Gaussian pseudo-randomness is the universal property of the compact hyperbolic spaces.

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