Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey


Authors: A. Peel, C.-A. Lin, F. Lanusse, A. Leonard, J.-L. Starck, M. Kilbinger
Journal: A&A
Year: 2017
Download: ADS | arXiv



Peak statistics in weak lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complement to two-point and higher-order statistics to constrain our cosmological models. To prepare for the high-precision data of next-generation surveys, we assess the constraining power of peak counts in a simulated Euclid-like survey on the cosmological parameters Ωm\Omega_\mathrm{m}, σ8\sigma_8, and w0dew_0^\mathrm{de}. In particular, we study how the Camelus model--a fast stochastic algorithm for predicting peaks--can be applied to such large surveys. We measure the peak count abundance in a mock shear catalogue of ~5,000 sq. deg. using a multiscale mass map filtering technique. We then constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation (ABC). We find that peak statistics yield a tight but significantly biased constraint in the σ8\sigma_8-Ωm\Omega_\mathrm{m} plane, indicating the need to better understand and control the model's systematics. We calibrate the model to remove the bias and compare results to those from the two-point correlation functions (2PCF) measured on the same field. In this case, we find the derived parameter Σ8=σ8(Ωm/0.27)α=0.76−0.03+0.02\Sigma_8=\sigma_8(\Omega_\mathrm{m}/0.27)^\alpha=0.76_{-0.03}^{+0.02} with α=0.65\alpha=0.65 for peaks, while for 2PCF the value is Σ8=0.76−0.01+0.02\Sigma_8=0.76_{-0.01}^{+0.02} with α=0.70\alpha=0.70. We therefore see comparable constraining power between the two probes, and the offset of their σ8\sigma_8-Ωm\Omega_\mathrm{m} degeneracy directions suggests that a combined analysis would yield tighter constraints than either measure alone. As expected, w0dew_0^\mathrm{de} cannot be well constrained without a tomographic analysis, but its degeneracy directions with the other two varied parameters are still clear for both peaks and 2PCF.


Effect of inhomogeneities on high precision measurements of cosmological distances


Authors: A. Peel, M. A. Troxel, M. Ishak
Journal: PRD
Year: 2014
Download: ADS | arXiv


We study effects of inhomogeneities on distance measures in an exact relativistic Swiss-cheese model of the Universe, focusing on the distance modulus. The model has Λ CDM background dynamics, and the "holes" are nonsymmetric structures described by the Szekeres metric. The Szekeres exact solution of Einstein's equations, which is inhomogeneous and anisotropic, allows us to capture potentially relevant effects on light propagation due to nontrivial evolution of structures in an exact framework. Light beams traversing a single Szekeres structure in different ways can experience either magnification or demagnification, depending on the particular path. Consistent with expectations, we find a shift in the distance modulus μ to distant sources due to demagnification when the light beam travels primarily through the void regions of our model. Conversely, beams are magnified when they propagate mainly through the overdense regions of the structures, and we explore a small additional effect due to time evolution of the structures. We then study the probability distributions of Δ μ = μΛCDMSC for sources at different redshifts in various Swiss-cheese constructions, where the light beams travel through a large number of randomly oriented Szekeres holes with random impact parameters. We find for Δμ the dispersions 0.004 ≤ σΔμ ≤ 0.008 mag for sources with redshifts 1.0 ≤ z ≤ 1.5 , which are smaller than the intrinsic dispersion of, for example, magnitudes of type Ia supernovae. The shapes of the distributions we obtain for our Swiss-cheese constructions are peculiar in the sense that they are not consistently skewed toward the demagnification side, as they are in analyses of lensing in cosmological simulations. Depending on the source redshift, the distributions for our models can be skewed to either the demagnification or the magnification side, reflecting a limitation of these constructions. This could be the result of requiring the continuity of Einstein's equations throughout the overall spacetime patchwork, which imposes the condition that compensating overdense shells must accompany the underdense void regions in the holes. The possibility to explore other uses of these constructions that could circumvent this limitation and lead to different statistics remains open.