Topology and the suppression of CMB large-angle correlations
  To date, no compelling evidence has been found that the universe has
non-trivial spatial topology. Meanwhile, anomalies in the observed CMB
temperature map, such as the lack of correlations at large angular separations,
remain observationally robust. We show that if our universe is flat and has one
compact dimension of appropriate size (slab topology), this would suppress
large-angle temperature correlations while maintaining a low-$\ell$ angular
power spectrum consistent with observations. The optimal length appears to be
$1.4$ times the conformal radius of the CMB's last scattering surface
($\chi_{rec}$). We construct the probability distribution function of the
statistic $S_{1/2}$ using simulated Sachs-Wolf-only skies for each of several
values of $L_z/\chi_{rec}$. For $L_z\simeq1.4\chi_{rec}$ the $p$-value of four
standard masked Planck maps is $p\simeq0.15$, compared to $p\lesssim0.003$ for
the conventional topologically trivial space. The mean angular power spectrum
$\langle C_{\ell} \rangle$ of the $L_z=1.4\chi_{rec}$ slab space matches the
observed power spectrum at $2\leq\ell\lesssim6$ -- including a substantially
suppressed quadrupole $C_2$, a slightly suppressed octopole $C_3$, and
unsuppressed higher multipoles. It does not predict other low-$\ell$ CMB
anomalies, and does not take account of normally sub-dominant Integrated Sachs
Wolfe contributions. An $L_z=1.4\chi_{rec}$ slab topology is consistent with
published limits from the Planck maps ($L_z\gtrsim1.12\chi_{rec}$). It is
within the 95% confidence range $1.2\leq L_z/\chi_{rec}\leq2.1$ inferred using
the covariance-matrix of temperature fluctuations. However, it violates
published circles-in-the-sky limits from WMAP and related unpublished limits
from Planck ($L_z/\chi_{rec}\gtrsim1.9$). We remark on the possibility to
satisfy these limits, and "postdict" other large-angle anomalies, with closely
related topologies.
