  We reexamine constraints on the spatial size of closed toroidal models with
cold dark matter and the cosmological constant from cosmic microwave
background. We carry out Bayesian analyses using the Cosmic Background Explorer
(COBE) data properly taking into account the statistically anisotropic
correlation, i.e., off-diagonal elements in the covariance. We find that the
COBE constraint becomes more stringent in comparison with that using only the
angular power spectrum, if the likelihood is marginalized over the orientation
of the observer. For some limited choices of orientations, the fit to the COBE
data is considerably better than that of the infinite counterpart. The best-fit
matter normalization is increased because of large-angle suppression in the
power and the global anisotropy of the temperature fluctuations. We also study
several deformed closed toroidal models in which the fundamental cell is
described by a rectangular box. In contrast to the cubic models, the
large-angle power can be enhanced in comparison with the infinite counterparts
if the cell is sufficiently squashed in a certain direction. It turns out that
constraints on some slightly deformed models are less stringent. We comment on
how these results affect our understanding of the global topology of our
universe.
