Are Compact Hyperbolic Models Observationally Ruled Out?

We revisit the observational constraints on compact(closed) hyperbolic(CH)models from cosmic microwave background(CMB). We carry out Bayesian analysesfor CH models with volume comparable to the cube of the present curvatureradius using the COBE-DMR data and show that a slight suppression in thelarge-angle temperature correlations owing to the non-trivial topology explainsrather naturally the observed anomalously low quadrupole which is incompatiblewith the prediction of the standard infinite Friedmann-Robertson-Walker models.While most of positions and orientations are ruled out, the likelihoods of CHmodels are found to be much better than those of infinite counterparts for somespecific positions and orientations of the observer, leading to less stringentconstraints on the volume of the manifolds. Even if the spatial geometry isnearly flat as $\Omega_{tot}=0.9-0.95$, suppression of the angular power onlarge angular scales is still prominent for CH models with volume much lessthan the cube of the present curvature radius if the cosmological constant isdominant at present.Comment: 25 pages, 16 EPS figures Version accepted for publication in PT