COMPUTING CMB ANISOTROPY IN COMPACT HYPERBOLIC SPACES

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to an d beyond the Hubble radius. For compact topologies, the two main effec ts on the CMB are: (i) the breaking of statistical isotropy in charact eristic patterns determined by the photon geodesic structure of the ma nifold and (ii) an infrared cut-off in the power spectrum of perturbat ions imposed by the finite spatial extent. We present a completely gen eral scheme using the regularized method of images for calculating CMB anisotropy in models with non-trivial topology, and apply it to the c omputationally challenging compact hyperbolic topologies. This new tec hnique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. We estimate a Bayesian probability for a selection of models by confronting the theoretical pixel-pixel temp erature correlation function with the COBE-DMR data. Our results demon strate that strong constraints on compactness arise: if the universe i s small compared to the 'horizon' size, correlations appear in the map s that are irreconcilable with the observations. If the universe is of comparable size, the likelihood function is very dependent upon orien tation of the manifold with respect to the sky. While most orientation s may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over the conventional infinite models.