Breaking the degeneracy: Optimal use of three-point weak lensing statistics

Abstract

We study the optimal use of three-point statistics in the analysis of weak lensing by large-scale structure. The three-point statistics statistics have long been advocated as a powerful tool to break measured degeneracies between cosmological parameters. Using ray-tracing simulations, incorporating important survey features such as a realistic depth-dependent redshift distribution, we find that a joint two-and three-point correlation function analysis is a much stronger probe of cosmology than the skewness statistic. We compare different observing strategies, showing that for a limited survey time there is an optimal depth for the measurement of three-point statistics, which balances statistical noise and cosmic variance against signal amplitude. We find that the chosen CFHTLS observing strategy was optimal and forecast that a joint two-and three-point analysis of the completed CFHTLS-Wide will constrain the amplitude of the matter power spectrum σ 8 to 10% and the matter density parameter Ω m to 17%, a factor of 2.5 improvement on the two-point analysis alone. Our error analysis includes all non-Gaussian terms, finding that the coupling between cosmic variance and shot noise is a non-negligible contribution which should be included in any future analytical error calculations.

Probing cosmology with weak lensing Minkowski functionals

“…This was already anticipated in [28], and is here clearly evidenced by the tighter constraints in the 2nd and 4th row in Figure 6, where multiple smoothing scales are combined. Also, [74] combined smoothing scales for the three-point auto-correlation function and most recently [55] confirmed the importance for peak counts as well. This is in sharp contrast to the power spectrum, where combining smoothing scales results in negligible improvements (as it should, at least in the linear regime).…”

“…Such a numerical calculation is beyond the scope of the present work, as well, and will be performed elsewhere. Instead, here we compare our results to the theoretical Fisher ellipse predictions obtained previously in [6,79], and the likelihood analysis for a related, simpler quantity, κ 3 , published in [74].…”

“…Varying the parameters Ω m and σ 8 , they find that combining the three-and two-point auto-correlation functions gives an improvement of a factor of ∼2.5 on the above parameters over the two-point auto-correlation function alone, for a CFHTLS-Wide-like survey. Although the auto-correlation functions appear dissimilar from the bispectrum and power spectrum, [74] combine 20 different smoothing scales for both κ 2 and κ 3 . Effectively, their set of twenty κ 2 's becomes a coarsely binned measure of the power spectrum with 20 bins in , while the set of κ 3 's remains an average over of the bispectrum over different triangle shapes.…”

“…Finally, [74] study a set of related statistical descriptors, namely κ 2 , κ 3 , and the skewness S 3 (κ). The first observational detection dark matter skewness was reported by [80].…”

“…The first observational detection dark matter skewness was reported by [80]. [74] take into account realistic survey configurations and study the effect of survey geometry (shallow/wide vs. deep/narrow) on the usefulness of these statistics. Varying the parameters Ω m and σ 8 , they find that combining the three-and two-point auto-correlation functions gives an improvement of a factor of ∼2.5 on the above parameters over the two-point auto-correlation function alone, for a CFHTLS-Wide-like survey.…”