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 compact cosmological models , one needs to compute eigenmodes of the Laplace-Beltrami operator .
We numerically obtain the eigenmodes on a compact 3-hyperbolic space cataloged as m 003 ( -2 , 3 ) in SnapPea SnapPea is a computer program by Jeff Weeks for creating and studying CH spaces [ ? ] . using the direct boundary element method , which enables one to simulate the CMB in multiply-connected compact models with high precision .
The angular power spectra C _ { l } ’ s ( 2 \leq l \leq 18 ) are calculated using computed eigenmodes for 5.4 \leq k < 10 and Gaussian random approximation for the expansion coefficients for 10 \leq k < 20 .
Assuming that the initial power spectrum is the Harrison-Zeldovich spectrum , the computed C _ { l } ’ s are consistent with the COBE data for 0.1 \leq \Omega _ { o } \leq 0.6 .
In low \Omega _ { o } models , the large-angular fluctuations can be produced at periods after the last scattering as the curvature perturbations decay in the curvature dominant era .