Deep redshift topological lensing: strategies for the T³ candidate

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The 3-torus (T³) FLRW model better fits the nearly zero large-scale auto-correlation of the WMAP CMB sky maps than the infinite flat model. The T³ model's WMAP parameters imply approximately equal-redshift topological lensing at z 6. We investigate observational strategies for rejecting the T³ solution or providing candidate topologically lensed galaxy pairs. T³ holonomies are applied to (i) existing z 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 T³ axis-centred northern and southern surveys if photometric redshift accuracy is σ() < 0.01 for a pair of nearly complete 100 deg² surveys with a total of > 500 galaxies over 4.3 < z < 6.6, or for a pair of 196 deg² surveys with > 400 galaxies and σ() < 0.02 over 4<z<7. Dropping the maximum time interval in a pair from Δt =1 Gyr/h to Δt =0.1 Gyr/h yields a requirement of σ() < 0.005 or σ() < 0.01, respectively. Millions of z 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.