Optimal Capture of Non-Gaussianity in Weak-Lensing Surveys: Power Spectrum, Bispectrum, and Halo Counts

Abstract

We compare the efficiency of weak lensing-selected galaxy clusters counts and of the weak lensing bispectrum at capturing non-Gaussian features in the dark matter distribution. We use the halo model to compute the weak lensing power spectrum, the bispectrum and the expected number of detected clusters, and derive constraints on cosmological parameters for a large, low systematic weak lensing survey, by focusing on the Ω m -σ 8 plane and on the dark energy equation of state. We separate the power spectrum into the resolved and the unresolved parts of the data, the resolved part being defined as detected clusters, and the unresolved part as the rest of the field. We consider four kinds of clusters counts, taking into account different amount of information : signal-to-noise ratio peak counts; counts as a function of clusters' mass; counts as a function of clusters' redshift; and counts as a function of clusters' mass and redshift. We show that when combined with the power spectrum, those four kinds of counts provide similar constraints, thus allowing one to perform the most direct counts, signalto-noise peaks counts, and get percent level constraints on cosmological parameters. We show that the weak lensing bispectrum gives constraints comparable to those given by the power spectrum and captures non-Gaussian features as well as clusters counts, its combination with the power spectrum giving errors on cosmological parameters that are similar to, if not marginally smaller than, those obtained when combining the power spectrum with cluster counts. We finally note that in order to reach its potential, the weak lensing bispectrum must be computed using all triangle configurations, as equilateral triangles alone do not provide useful information. The appendices summarize the halo model, and the way the power spectrum and bispectrum are computed in this framework.

Probing cosmology with weak lensing Minkowski functionals

“…The solid (dashed) ellipse uses backward (forward) finite differences. The agreement between both the orientation and overall size of our error ellipse and that shown in Figure 5 of [8] is very good, especially considering that theirs is for a different cosmology with (Ω m , σ 8 ) = (0.3, 0.9). Ours is a factor of 1.25 larger in Ω m and a factor of 1.4 in σ 8 .…”

“…While there are many other previous estimates for cosmological constraints from the WL power spectrum (e.g. [42], and for a very recent study, examining constraints from power spectrum of the logarithm of the convergence field, see [70]) the specifications in the study by [8] are closest to the present work. In particular, those authors present a two-dimensional Fisher ellipse, in Figure 5 of their paper, in which they vary only the two parameters Ω m and σ 8 .…”

“…The center features an IBM Blue Gene/L with 36,864 CPUs and a Blue Gene/P with 8,192 CPUs. We ran a series of 80 CDM N -body simulations with 512 3 particles each and a box size of 240h −1 Mpc.…”

“…Therefore, the MFs appear particularly useful to improve constrains on dark energy. 8 We would next like to understand the origin of these constraints better. Looking at the leftmost panel of the first row in Figure 6, we see that the power spectrum has a degeneracy in the (w, σ 8 )-direction.…”

“…This is because gravity is non-linear, and it generates nonGaussianity on small scales. Perhaps the most natural way to proceed and characterize non-Gaussian statistical signatures is by using higher-order poly-spectra [1], or equivalently, three-point and higher-order correlation functions [2][3][4][5][6][7][8][9][10]. 1 An interesting, and less explored alternative, originally suggested in the context of the cosmic density field [12], is to utilize topological features.…”