COBE constraints on a compact toroidal low-density universe

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 \Λ-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 \Ωₘ=0.1 and \Ω_\Λ=0.9 whereas N\~8 for \Ωₘ=1.0 and \Ω_\Λ=0.