Deep redshift topological lensing: strategies for the T^3 candidate

TL;DR

This paper explores observational strategies to test the 3-torus (T^3) cosmological model using galaxy surveys and topological lensing signatures, aiming to confirm or reject the model with future data.

Contribution

It proposes a method to detect or rule out the T^3 topology by analyzing galaxy catalogues and quadruple statistics, providing specific observational criteria for future surveys.

Findings

Detection possible with <0.01 photometric redshift accuracy

Rejection or confirmation depends on survey size and redshift precision

Millions of galaxies will enable stronger constraints in coming decades

Abstract

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.