Are Compact Hyperbolic Models Observationally Ruled Out?

Abstract

We revisit the observational constraints on compact(closed) hyperbolic(CH) models from cosmic microwave background(CMB). We carry out Bayesian analyses for CH models with volume comparable to the cube of the present curvature radius using the COBE-DMR data and show that a slight suppression in the large-angle temperature correlations owing to the non-trivial topology explains rather naturally the observed anomalously low quadrupole which is incompatible with the prediction of the standard infinite Friedmann-Robertson-Walker models. While most of positions and orientations are ruled out, the likelihoods of CH models are found to be much better than those of infinite counterparts for some specific positions and orientations of the observer, leading to less stringent constraints on the volume of the manifolds. Even if the spatial geometry is nearly flat as $Ω_{tot}=0.9-0.95$, suppression of the angular power on large angular scales is still prominent for CH models with volume much less than the cube of the present curvature radius if the cosmological constant is dominant at present.