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 $Λ$-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 $Ω_m=0.1$ and $Ω_Λ=0.9$ whereas $N\sim8$ for $Ω_m=1.0$ and $Ω_Λ=0$.