Deep redshift topological lensing: strategies for the T^3 candidate
  The 3-torus (T^3) FLRW model better fits the nearly zero large-scale
auto-correlation of the WMAP CMB sky maps than the infinite flat model. The T^3
model's WMAP parameters imply approximately equal-redshift topological lensing
at z \sim 6. We investigate observational strategies for rejecting the T^3
solution or providing candidate topologically lensed galaxy pairs. T^3
holonomies are applied to (i) existing z \sim 6 observations and (ii) simulated
observations, creating multiply connected catalogues. Corresponding simply
connected catalogues are generated. Each catalogue is analysed using a
successive filter method and collecting matched quadruples. Quadruple
statistics between the multiply and simply connected catalogues are compared.
The expected rejection of the hypothesis, or detection of candidate
topologically lensed galaxies, is possible at a significance of 5% for a pair
of T^3 axis-centred northern and southern surveys if photometric redshift
accuracy is \sigma(\zphot) < 0.01 for a pair of nearly complete 100 deg^2
surveys with a total of > 500 galaxies over 4.3 < z < 6.6, or for a pair of 196
deg^2 surveys with > 400 galaxies and \sigma(\zphot) < 0.02 over 4<z<7.
Dropping the maximum time interval in a pair from \Delta t =1 Gyr/h to \Delta t
=0.1 Gyr/h yields a requirement of \sigma(\zphot) < 0.005 or \sigma(\zphot) <
0.01, respectively. Millions of z \sim 6 galaxies will be observed over fields
of these sizes during the coming decades, implying much stronger constraints.
The question is not if the hypothesis will be rejected or confirmed, it is
when.
