Probing cosmology with weak lensing Minkowski functionals

Abstract

In this paper, we show that Minkowski Functionals (MFs) of weak gravitational lensing (WL) convergence maps contain significant non-Gaussian, cosmology-dependent information. To do this, we run a large suite of cosmological ray-tracing N-body simulations to create mock weak WL convergence maps, and study the cosmological information content of MFs derived from these maps. Our suite consists of 80 independent 512 3 N-body runs, covering seven different cosmologies, varying three cosmological parameters Ωm, w, and σ8 one at a time, around a fiducial ΛCDM model. In each cosmology, we use ray-tracing to create a thousand pseudo-independent 12 deg 2 convergence maps, and use these in a Monte Carlo procedure to estimate the joint confidence contours on the above three parameters. We include redshift tomography at three different source redshifts zs = 1, 1.5, 2, explore five different smoothing scales θG = 1, 2, 3, 5, 10 arcmin, and explicitly compare and combine the MFs with the WL power spectrum. We find that the MFs capture a substantial amount of information from non-Gaussian features of convergence maps, i.e. beyond the power spectrum. The MFs are particularly well suited to break degeneracies and to constrain the dark energy equation of state parameter w (by a factor of ≈ three better than from the power spectrum alone). The non-Gaussian information derives partly from the one-point function of the convergence (through V0, the "area" MF), and partly through non-linear spatial information (through combining different smoothing scales for V0, and through V1 and V2, the boundary length and genus MFs, respectively). In contrast to the power spectrum, the best constraints from the MFs are obtained only when multiple smoothing scales are combined.

Impact of Baryonic Processes on Weak-Lensing Cosmology: Power Spectrum, Nonlocal Statistics, and Parameter Bias

“…Overall, PS is the most studied statistic, and it is intuitively easy to understand based on physics; P ℓ ( ) k is a direct measure of the fluctuations at a given scale ℓ. Although some numerical studies (Kratochvil et al 2012;Shirasaki & Yoshida 2014) suggest that nonlocal statistics would be useful to make tight cosmological constraints, there are intrinsic difficulties to derivinganalytical models for MFs and peak counts. Hence, it is not straightforward to interpret the nonlocal statistics and their dependence on cosmological parameters.…”

“…For discretized  maps, we employ the following estimators, as shown in, e.g., Kratochvil et al (2012):…”

“…MFs are morphological statistics for a given multidimensional field. MFs are one of the good measures of topology in WL and contain the suitable cosmological information beyond twopoint statistics (Kratochvil et al 2012;Munshi et al 2012;Shirasaki et al 2012;Shirasaki & Yoshida 2014). Throughout this paper, we use the terms "local statistics" and "nonlocal statistics."…”

Sample variance in weak lensing: How many simulations are required?

“…In an era where cosmology is data driven, accurate numerical simulations of shear fields are becoming important for several reasons, including assessing baryonic effects [9][10][11][12][13][14], the utility of non-Gaussian statistics [15][16][17][18][19][20][21][22][23] and various systematic effects [24][25][26][27].…”

Masked Areas in Shear Peak Statistics: A Forward Modeling Approach

“…Beyond simply counting peaks in simulated shear maps, Kratochvil et al (2012), Petri et al (2013) and Shirasaki et al (2013) have used Minkowski functionals to extract more information from reconstructed convergence maps produced from cosmological N-body simulations. In a similar vein, Marian et al (2013) introduced statistics beyond the peak abundance to further constrain cosmology, including peakpeak correlation functions.…”