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Register a new userCosmology Constraints from the Weak Lensing Peak Counts and the Power Spectrum in CFHTLenS
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Jia Liu
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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 $sigma_8(Omega_m/0.27)^{0.63}=0.85substack{+0.03 -0.03}$.
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We propose counting peaks in weak lensing (WL) maps, as a function of their height, to probe models of dark energy and to constrain cosmological parameters. Because peaks can be identified in two-dimensional WL maps directly, they can provide constraints that are free from potential selection effects and biases involved in identifying and determining the masses of galaxy clusters. We have run cosmological N-body simulations to produce WL convergence maps in three models with different constant values of the dark energy equation of state parameter, w=-0.8, -1, and -1.2, with a fixed normalization of the primordial power spectrum (corresponding to present-day normalizations of sigma8=0.742, 0.798, and 0.839, respectively). By comparing the number of WL peaks in 8 convergence bins in the range of -0.1 < kappa < 0.2, in multiple realizations of a single simulated 3x3 degree field, we show that the first (last) pair of models can be distinguished at the 95% (85%) confidence level. A survey with depth and area (20,000 sq. degrees), comparable to those expected from LSST, should have a factor of approx. 50 better parameter sensitivity. We find that relatively low-amplitude peaks (kappa = 0.03), which typically do not correspond to a single collapsed halo along the line of sight, account for most of this sensitivity. We study a range of smoothing scales and source galaxy redshifts (z_s). With a fixed source galaxy density of 15/arcmin^2, the best results are provided by the smallest scale we can reliably simulate, 1 arcminute, and z_s=2 provides substantially better sensitivity than z_s< 1.5.
In order to extract full cosmological information from next-generation large and high-precision weak lensing (WL) surveys (e.g. Euclid, Roman, LSST), higher-order statistics that probe the small-scale, non-linear regime of large scale structure (LSS) need to be utilized. WL peak counts, which trace overdensities in the cosmic web, are one promising and simple statistic for constraining cosmological parameters. The physical origin of WL peaks have previously been linked to dark matter halos along the line of sight and this peak-halo connection has been used to develop various semi-analytic halo-based models for predicting peak counts. Here, we study the origin of WL peaks and the effectiveness of halo-based models for WL peak counts using a suite of ray-tracing N-body simulations. We compare WL peaks in convergence maps from the full simulations to those in maps created from only particles associated with halos -- the latter playing the role of a perfect halo model. We find that while halo-only contributions are able to replicate peak counts qualitatively well, halos do not explain all WL peaks. Halos particularly underpredict negative peaks, which are associated with local overdensities in large-scale underdense regions along the line of sight. In addition, neglecting non-halo contributions to peaks counts leads to a significant bias on the parameters ($Omega_{rm m}$, $sigma_{8}$) for surveys larger than $geq$ 100 deg$^{2}$. We conclude that other elements of the cosmic web, outside and far away from dark matter halos, need to be incorporated into models of WL peaks in order to infer unbiased cosmological constraints.
The statistics of peaks in weak lensing convergence maps is a promising tool to investigate both the properties of dark matter haloes and constrain the cosmological parameters. We study how the number of detectable peaks and its scaling with redshift depend upon the cluster dark matter halo profiles and use peak statistics to constrain the parameters of the mass - concentration (MC) relation. We investigate which constraints the Euclid mission can set on the MC coefficients also taking into account degeneracies with the cosmological parameters. To this end, we first estimate the number of peaks and its redshift distribution for different MC relations. We find that the steeper the mass dependence and the larger the normalisation, the higher is the number of detectable clusters, with the total number of peaks changing up to $40%$ depending on the MC relation. We then perform a Fisher matrix forecast of the errors on the MC relation parameters as well as cosmological parameters. We find that peak number counts detected by Euclid can determine the normalization $A_v$, the mass $B_v$ and redshift $C_v$ slopes and intrinsic scatter $sigma_v$ of the MC relation to an unprecedented accuracy being $sigma(A_v)/A_v = 1%$, $sigma(B_v)/B_v = 4%$, $sigma(C_v)/C_v = 9%$, $sigma(sigma_v)/sigma_v = 1%$ if all cosmological parameters are assumed to be known. Should we relax this severe assumption, constraints are degraded, but remarkably good results can be restored setting only some of the parameters or combining peak counts with Planck data. This precision can give insight on competing scenarios of structure formation and evolution and on the role of baryons in cluster assembling. Alternatively, for a fixed MC relation, future peaks counts can perform as well as current BAO and SNeIa when combined with Planck.
Weak gravitational lensing is a powerful cosmological probe, with non--Gaussian features potentially containing the majority of the information. We examine constraints on the parameter triplet $(Omega_m,w,sigma_8)$ from non-Gaussian features of the weak lensing convergence field, including a set of moments (up to $4^{rm th}$ order) and Minkowski functionals, using publicly available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of ray--tracing N-body simulations spanning 91 points in $(Omega_m,w,sigma_8)$ parameter space, replicating the galaxy sky positions, redshifts and shape noise in the CFHTLenS catalogs. We then build an emulator that interpolates the simulated descriptors as a function of $(Omega_m,w,sigma_8)$, and use it to compute the likelihood function and parameter constraints. We employ a principal component analysis to reduce dimensionality and to help stabilize the constraints with respect to the number of bins used to construct each statistic. Using the full set of statistics, we find $Sigma_8equivsigma_8(Omega_m/0.27)^{0.55}=0.75pm0.04$ (68% C.L.), in agreement with previous values. We find that constraints on the $(Omega_m,sigma_8)$ doublet from the Minkowski functionals suffer a strong bias. However, high-order moments break the $(Omega_m,sigma_8)$ degeneracy and provide a tight constraint on these parameters with no apparent bias. The main contribution comes from quartic moments of derivatives.
We present measurements of the weak gravitational lensing shear power spectrum based on $450$ sq. deg. of imaging data from the Kilo Degree Survey. We employ a quadratic estimator in two and three redshift bins and extract band powers of redshift auto-correlation and cross-correlation spectra in the multipole range $76 leq ell leq 1310$. The cosmological interpretation of the measured shear power spectra is performed in a Bayesian framework assuming a $Lambda$CDM model with spatially flat geometry, while accounting for small residual uncertainties in the shear calibration and redshift distributions as well as marginalising over intrinsic alignments, baryon feedback and an excess-noise power model. Moreover, massive neutrinos are included in the modelling. The cosmological main result is expressed in terms of the parameter combination $S_8 equiv sigma_8 sqrt{Omega_{rm m}/0.3}$ yielding $S_8 = 0.651 pm 0.058$ (3 z-bins), confirming the recently reported tension in this parameter with constraints from Planck at $3.2sigma$ (3 z-bins). We cross-check the results of the 3 z-bin analysis with the weaker constraints from the 2 z-bin analysis and find them to be consistent. The high-level data products of this analysis, such as the band power measurements, covariance matrices, redshift distributions, and likelihood evaluation chains are available at http://kids.strw.leidenuniv.nl/
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