Deep redshift topological lensing: strategies for the T3 candidate

The 3-torus (T3) Friedmann–Lemaître–Robertson–Walker model better fits the nearly zero large-scale two-point auto-correlation of the Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background sky maps than the infinite flat model. The T3 model's parameters, recently found using an optimal cross-correlation method on WMAP data, imply approximately equal-redshift topological lensing at redshifts z ∼ 6, the redshift range of the upcoming generation of new instruments and telescopes. We investigate observational strategies that can reject the T3 solution for a given region of parameter space of physical assumptions, or provide good candidate topologically lensed galaxy pairs for detailed spectroscopic followup. T3 holonomies are applied to (i) existing z ∼ 6 observations and (ii) simulated observations, creating multiply connected catalogues. Corresponding simply connected catalogues are generated. The simulated observational strategies are motivated by the matched discs principle. 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 per cent for a pair of T3 axis-centred northern and southern surveys if photometric redshift accuracy is σ(zphot) ≲ 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(zphot) ≲ 0.02 over 4 < z < 7. Dropping the maximum time interval in a pair from Δt = 1 h−1 Gyr to Δt = 0.1 h−1 Gyr requires σ(zphot) ≲ 0.005 or σ(zphot) ≲ 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.