ar X iv : a st ro - p h / 98 04 04 2 v 1 4 A pr 1 99 8 CITA - 98 - 11 Probing Cosmic topology using CMB anisotropy

The measurements of CMB anisotropy have opened up a window for probing the global topol-ogy of the universe on length scales comparable to and beyond the Hubble radius. We have developed a new method for calculating the CMB anisotropy in models with nontrivial topol-ogy and apply it to open universe models with compact spatial topology. We conduct a Bayesian probability analysis for a selection of models which confronts the theoretical pixel-pixel temperature correlation function with the cobe–dmr data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the 'horizon' size, correlations appear in the maps that are irreconcilable with the observations. The remarkable degree of isotropy of the cosmic microwave background (CMB) points to homogeneous and isotropic Friedmann-Robertson-Walker (FRW) models for the universe. This argument is a purely local one and does not refer to the global topological structure of the universe. In fact, in the absence of spatially inhomogeneous perturbations, a FRW model predicts an isotropic CMB regardless of the global topological structure. However, the observed large scale structure in the universe and CMB anisotropy allude to the existence of small spatially inhomogeneous primordial perturbations. The global topology of the universe does affect the observable properties of the CMB anisotropy. In compact universe models, the finite spatial size usually implies a suppression of the power in large scale perturbations and consequently the CMB anisotropy is suppressed on angular scales above a characteristic angle related to size of the universe. Another signature is the breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the compact manifold. Much recent astrophysical data suggest the cosmological density parameter, Ω 0 , is subcriti-cal. 1 In the absence of a cosmological constant, this would imply a hyperbolic spatial geometry for the universe (commonly referred to as the 'open' universe in cosmological literature). The topologically trivial (simply connected) hyperbolic 3-space, H 3 , is non-compact and has infinite size. There are numerous theoretical motivations, however, to favor a spatially compact