The size of the Universe according to the Poincare dodecahedral space
  hypothesis
  One of the FLRW models that best fits the WMAP sky maps of the CMB is the
Poincare dodecahedral space. The optimal fit of this model to WMAP data was
recently found using an optimal cross-correlation method, but the systematic
error in the estimate of the matched-circle angular radius \alpha, or
equivalently, the (comoving) size of the Universe 2\rinj (twice the injectivity
radius), might be much higher than the random error. In order to increase the
falsifiability of the model, it would be useful to reduce the uncertainty in
this estimate and to estimate the fraction of the sky where multiply imaged
gravitationally bound objects should potentially be detectable. "Matched discs"
are defined in order to describe a useful subset of multiply imaged objects.
The cross-correlation method at \ltapprox 1 \hGpc is applied to WMAP 7-year
data in order to improve the estimate of \alpha. The improved matched-circle
radius estimate is \alpha = 23 \pm 1.4 deg, where the uncertainty represents
systematic error dependent on the choices of galactic mask and all-sky map.
This is equivalent to 2\rinj = 18.2\pm 0.5 \hGpc for matter density parameter
Omega_m=0.28\pm 0.02. The lowest redshift of multiply imaged objects is
z=106\pm18. Multiply imaged high overdensity (rare) peaks visible during
200>z>106 should be present in matched discs of radius 14.8\pm2.3 deg. The
accuracy in the matched circle radius estimate is considerably improved by
using the higher resolution signal. The predicted matched discs (over
200>z>106) project to about 20% of the full sky. Since any object located
exactly in the discs would be multiply imaged at equal redshifts, evolutionary
effects would be small for objects that are nearly located in the discs.
