COBE Constraints on a Compact Toroidal Low-density Universe

Abstract

In this paper, the cosmic microwave background (CMB) anisotropy in a multiply-connected compact flat 3-torus model with the cosmological constant is investigated. Using the COBE-DMR 4-year data, a full Bayesian analysis revealed that the constraint on the topology of the flat 3-torus model with low-matter-density is less stringent. As in compact hyperbolic models, the large-angle temperature fluctuations can be produced as the gravitational potential decays at the $\Lambda$-dominant epoch well after the last scattering. The maximum allowed number $N$ of images of the cell (fundamental domain) within the observable region at present is approximately 49 for ${\Omega }_m=0.1$ and ${\Omega }_{\Lambda }=0.9$ whereas $N\sim 8$ for ${\Omega }_m=1.0$ and ${\Omega }_{\Lambda }=0$.

13 pages using RevTeX, 5 eps files, typos corrected

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• Cosmic microwave background constraints on multi-connected spherical spaces
• A Topological Signature in Cosmic Topology
• Topology beyond the horizon: how far can it be probed?
• Topological signatures in CMB temperature anisotropy maps
• On the detectability of non-trivial topologies
• How large is our universe?
• Topology of the universe from COBE-DMR; a wavelet approach
• Determining the shape of the Universe using discrete sources