Studying the LSS through weak gravitational lensing maps

Weak gravitational lensing is a promising tool for the study of the mass distribution in the Universe. Here we report some partial results that show how lensing maps can be used to differentiate between cosmological models. We pay special attention to the role of noise and smoothing. As an application, we use mock convergence fields constructed from N-body simulations of the large-scale structure for three historically important cosmological models. Various map analyses are used, including Minkowski functionals, and their ability to differentiate the models is calculated and discussed. The images of distant galaxies are tangentially stretched in relation to mass concentrations in its light path. This weak gravitational lensing effect can be statistically measured and enables the construction of “lensing maps” (see Bartelmann & Schneider 2001 for a review of weak gravitational lensing). Here we focus on the convergence field κ, which can be calculated using κ(~θ) = 3H o 2 Ωm ∫ z 0 g(z′, z) δ(~θ, z) a(z) dz′ , (1) where ~θ is the angular position at the map, g a geometrical weighting factor, δ the density contrast, and a the scale factor. This map contains information about the large-scale structure of the Universe (LSS). Our aim is to relate the characteristics of the convergence field to the LSS (see Jain, Seljak, & White 2000), and to discuss the ability of analyses of the convergence to differentiate between cosmological models. Our approach is to simulate κ(~θ) and use various statistics to characterize it. We used N-body simulations (Hydra code Couchman, Thomas, & Pearce 1995 with 128 cold dark matter particles in boxes of side 128hMpc) to create realizations of the LSS between z = 0 and a source redshift z = 1. A multiple-plane lens approximation to equation (1) was them used to generate 25 realizations of the convergence field. We considered three models: SCDM (Ωm = 1, σ8 = 0.56), ΛCDM (Ωm = 0.3, ΩΛ = 0.7, σ8 = 0.99), and OCDM (Ωm = 0.3, ΩΛ = 0, σ8 = 0.84). The indicated σ8 represents a normalization to the cluster abundance, and we adopt h = 0.7. The generated fields had a minimum size of 9.6 degrees, in a 1024 grid. We used a top-hat window of radius θs to smooth the convergence field, and quantified it by calculating statistical measures. These included the convergence More complete and detailed results will be published elsewhere 1 2 Antonio C. C. Guimarães −0.04 −0.02 0 0.02 0.0 20.0 40.0 pd f ΛCDM SCDM OCDM 0.0 20.0 40.0 60.0