CMB anisotropy in compact hyperbolic universes. II. COBE maps and limits -art. no. 043006

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to, and even be yond, the Hubble radius. For compact topologies, the two main effects on th e CMB are: (1) the breaking of statistical isotropy in characteristic patte rns determined by the photon geodesic structure of the manifold and (2) an infrared cutoff in the power spectrum of perturbations imposed by the finit e spatial extent. We calculate the CMB anisotropy in compact hyperbolic uni verse models using the regularized method of images described in detail in the preceding paper, including the line-of-sight "integrated Sachs-Wolfe" e ffect, as well as the last-scattering surface terms. We calculate the Bayes ian probabilities fur a selection of models by confronting our theoretical pixel-pixel temperature correlation functions with the COBE-DMR data. Our r esults demonstrate that strong constraints on compactness arise: if the uni verse is small compared to the horizon size, correlations appear in the map s that are irreconcilable with the observations. This conclusion is qualita tively insensitive to the matter content of the universe, in particular, th e presence of cosmological constant. If the universe is of comparable size to the "horizon," the likelihood function is very dependent upon orientatio n of the manifold w.r.t. the sky. While most orientations may be strongly r uled out, it sometimes happens that for a specific orientation the predicte d correlation patterns are preferred over those fur the conventional infini te models. The full Bayesian analysis we use is the most complete statistic al test that can be done on the cosmic background explorer maps, taking int o account all possible signals and their variances in the theoretical skies , in particular the high degree of anisotropic correlation that can exist. We also show that standard visual measures for comparing theoretical predic tions with the data such as the isotropized power spectrum C-l are not so u seful in small compact spaces because of enhanced cosmic variance associate d with the breakdown of statistical isotropy.