CMB Anisotropy in Compact Hyperbolic Universes

Details CMB Anisotropy in Compact Hyperbolic Universes CMB Anisotropy in Compact Hyperbolic Universes

1999-03-30

arxiv.org/abs/astro-ph/9903446v2

Astronomy and Astrophysics

Astrophysics

4 pages, 1 EPS figure, to appear in AIP Conference Proceedings "3K Cosmology" held in Rome, Oct 5-10, 1998, edited by Luciano

Scientific paper

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 $m003(-2,3)$ in SnapPea (computer program by Jeff Weeks) 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 ($2 \leq l\leq18$) are calculated using computed eigenmodes for $5.4\leqk<10$ and Gaussian random approximation for the expansion coefficients for $10\leqk<20$. 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.

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