The size of the Universe according to the Poincare dodecahedral space hypothesis

TL;DR

This paper refines the estimate of the Universe's size under the Poincare dodecahedral space hypothesis using WMAP data, reducing uncertainties and predicting where multiply imaged objects should be detectable.

Contribution

It improves the systematic error estimate of the Universe's size in the Poincare model and identifies regions where multiply imaged objects are likely to be found.

Findings

Matched-circle radius estimated at 23 ± 1.4 degrees.

Corresponding Universe size is 18.2 ± 0.5 hGpc.

Matched discs cover about 20% of the sky.

Abstract

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.