A spatial-correlation analysis of the cubic 3-torus topology based on
  the Planck 2013 data
  Spatial correlations of the cubic 3-torus topology are analysed using the
Planck 2013 data. The spatial-correlation method for detecting multiply
connected spaces is based on the fact that positions on the cosmic microwave
background (CMB) sky, that are separated by large angular distances, can be
spatially much nearer according to a hypothesized topology. The comparison of
the correlations computed with and without the assumed topology can reveal
whether a promising topological candidate is found. The level of the expected
correlations is estimated by CMB simulations of the cubic 3-torus topology and
compared to those obtained from the Planck data. An interesting 3-torus
configuration is discovered which possesses topological correlations of the
magnitude found in the CMB simulations based on a toroidal universe. Although
the spatial-correlation method has a high false-positive rate, it is striking
that there exists an orientation of a cubic 3-torus cell, where correlations
between points that are separated by large angular distances, mimic those of
closely separated points.
