Cosmology Constraints from the Weak Lensing Peak Counts and the Power Spectrum in CFHTLenS

TL;DR

This study demonstrates that weak lensing peak counts, when combined with the power spectrum, provide competitive and improved constraints on cosmological parameters, utilizing simulations and an emulator to analyze CFHTLenS data.

Contribution

The paper introduces a new approach combining peak counts and power spectrum in weak lensing analysis, with an emulator for accurate interpolation across cosmological models.

Findings

Peak counts constraints are comparable to power spectrum constraints.

Combining both observables tightens parameter constraints significantly.

Constraints on $w$ require external data; combined analysis improves $\sigma_8$ and $\Omega_m$ estimates.

Abstract

Lensing peaks have been proposed as a useful statistic, containing cosmological information from non-Gaussianities that is inaccessible from traditional two-point statistics such as the power spectrum or two-point correlation functions. Here we examine constraints on cosmological parameters from weak lensing peak counts, using the publicly available data from the 154 deg$^2$ CFHTLenS survey. We utilize a new suite of ray-tracing N-body simulations on a grid of 91 cosmological models, covering broad ranges of the three parameters $\Omega_m$, $\sigma_8$, and $w$, and replicating the Galaxy sky positions, redshifts, and shape noise in the CFHTLenS observations. We then build an emulator that interpolates the power spectrum and the peak counts to an accuracy of $\leq 5\%$, and compute the likelihood in the three-dimensional parameter space ($\Omega_m$, $\sigma_8$, $w$) from both observables. We find that constraints from peak counts are comparable to those from the power spectrum, and somewhat tighter when different smoothing scales are combined. Neither observable can constrain $w$ without external data. When the power spectrum and peak counts are combined, the area of the error "banana'' in the ($\Omega_m$, $\sigma_8$) plane reduces by a factor of $\approx2$, compared to using the power spectrum alone. For a flat $\Lambda$ cold dark matter model, combining both statistics, we obtain the constraint $\sigma_8(\Omega_m/0.27)^{0.63}=0.85\substack{+0.03 \\ -0.03}$.