Imprints of primordial non-Gaussianity on the number counts of cosmic shear peaks

We studied the effect of primordial non-Gaussianity with varied bispectrum shapes on the number counts of signal-to-noise peaks in wide field cosmic shear maps. The two cosmological contributions to this particular weak lensing statistic, namely the chance projection of Large Scale Structure and the occurrence of real, cluster-sized dark matter halos, have been modeled semi-analytically, thus allowing to easily introduce the effect of non-Gaussian initial conditions. We performed a Fisher matrix analysis by taking into account the full covariance of the peak counts in order to forecast the joint constraints on the level of primordial non-Gaussianity and the amplitude of the matter power spectrum that are expected by future wide field imaging surveys. We find that positive-skewed non-Gaussianity increases the number counts of cosmic shear peaks, more so at high signal-to-noise values, where the signal is mostly dominated by massive clusters as expected. The increment is at the level of ~1 for f_NL=10 and ~10 for f_NL=100 for a local shape of the primordial bispectrum, while different bispectrum shapes give generically a smaller effect. For a future survey on the model of the proposed ESA space mission Euclid and by avoiding the strong assumption of being capable to distinguish the weak lensing signal of galaxy clusters from chance projection of Large Scale Structures we forecasted a 1-sigma error on the level of non-Gaussianity of ~30-40 for the local and equilateral models, and of ~100-200 for the less explored enfolded and orthogonal bispectrum shapes.Comment: 13 pages, 8 figures, 1 table. Submitted to MNRA

An analytic approach to number counts of weak-lensing peak detections

We develop and apply an analytic method to predict peak counts in weak-lensing surveys. It is based on the theory of Gaussian random fields and suitable to quantify the level of spurious detections caused by chance projections of large-scale structures as well as the shape and shot noise contributed by the background galaxies. We compare our method to peak counts obtained from numerical ray-tracing simulations and find good agreement at the expected level. The number of peak detections depends substantially on the shape and size of the filter applied to the gravitational shear field. Our main results are that weak-lensing peak counts are dominated by spurious detections up to signal-to-noise ratios of 3--5 and that most filters yield only a few detections per square degree above this level, while a filter optimised for suppressing large-scale structure noise returns up to an order of magnitude more.Comment: 9 pages, 5 figures, submitted to A&

Searching dark-matter halos in the GaBoDS survey

We apply the linear filter for the weak-lensing signal of dark-matter halos developed in Maturi et al. (2005) to the cosmic-shear data extracted from the Garching-Bonn-Deep-Survey (GaBoDS). We wish to search for dark-matter halos through weak-lensing signatures which are significantly above the random and systematic noise level caused by intervening large-scale structures. We employ a linear matched filter which maximises the signal-to-noise ratio by minimising the number of spurious detections caused by the superposition of large-scale structures (LSS). This is achieved by suppressing those spatial frequencies dominated by the LSS contamination. We confirm the improved stability and reliability of the detections achieved with our new filter compared to the commonly-used aperture mass (Schneider, 1996; Schneider et al., 1998) and to the aperture mass based on the shear profile expected for NFW haloes (see e.g. Schirmer et al., 2004; Hennawi & Spergel, 2005). Schirmer et al.~(2006) achieved results comparable to our filter, but probably only because of the low average redshift of the background sources in GaBoDS, which keeps the LSS contamination low. For deeper data, the difference will be more important, as shown by Maturi et al. (2005). We detect fourteen halos on about eighteen square degrees selected from the survey. Five are known clusters, two are associated with over-densities of galaxies visible in the GaBoDS image, and seven have no known optical or X-ray counterparts.Comment: 8 pages, 4 figures, accepted by A&

Cosmological Parameter Estimation from SN Ia data: a Model-Independent Approach

We perform a model independent reconstruction of the cosmic expansion rate based on type Ia supernova data. Using the Union 2.1 data set, we show that the Hubble parameter behaviour allowed by the data without making any hypothesis about cosmological model or underlying gravity theory is consistent with a flat LCDM universe having H_0 = 70.43 +- 0.33 and Omega_m=0.297 +- 0.020, weakly dependent on the choice of initial scatter matrix. This is in closer agreement with the recently released Planck results (H_0 = 67.3 +- 1.2, Omega_m = 0.314 +- 0.020) than other standard analyses based on type Ia supernova data. We argue this might be an indication that, in order to tackle subtle deviations from the standard cosmological model present in type Ia supernova data, it is mandatory to go beyond parametrized approaches

Deconvolution with Shapelets

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.Comment: 9 pages, 9 figures, submitted to A&

Optimal filtering of optical and weak lensing data to search for galaxy clusters: application to the COSMOS field

Galaxy clusters are usually detected in blind optical surveys via suitable filtering methods. We present an optimal matched filter which maximizes their signal-to-noise ratio by taking advantage of the knowledge we have of their intrinsic physical properties and of the data noise properties. In this paper we restrict our application to galaxy magnitudes, positions and photometric redshifts if available, and we also apply the filter separately to weak lensing data. The method is suitable to be naturally extended to a multi-band approach which could include not only additional optical bands but also observables with different nature such as X-rays. For each detection, the filter provides its significance, an estimate for the richness and for the redshift even if photo-z are not given. The provided analytical error estimate is tested against numerical simulations. We finally apply our method to the COSMOS field and compare the results with previous cluster detections obtained with different methods. Our catalogue contains 27 galaxy clusters with minimal threshold at 3-sigma level including both optical and weak-lensing information.Comment: 15 pages, 15 figures, accepted for publication in MNRA

An optimal filter for the detection of galaxy clusters through weak lensing

We construct a linear filter optimised for detecting dark-matter halos in weak-lensing data. The filter assumes a mean radial profile of the halo shear pattern and modifies that shape by the noise power spectrum. Aiming at separating dark-matter halos from spurious peaks caused by large-scale structure lensing, we model the noise as being composed of weak lensing by large-scale structures and Poisson noise from random galaxy positions and intrinsic ellipticities. Optimal filtering against the noise requires the optimal filter scale to be smaller than typical halo sizes. Although a perfect separation of halos from spurious large-scale structure peaks is strictly impossible, we use numerical simulations to demonstrate that our filter produces substantially more sensitive, reliable and stable results than the conventionally used aperture-mass statistic.Comment: 9 pages, 6 figures, A&A submitte

Nonparametric predictive inference for diagnostic test thresholds

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine, machine learning and credit scoring. The receiver operating characteristic (ROC) curve and surface are useful tools to assess the ability of diagnostic tests to discriminate between ordered classes or groups. To define these diagnostic tests, selecting the optimal thresholds that maximize the accuracy of these tests is required. One procedure that is commonly used to find the optimal thresholds is by maximizing what is known as Youden’s index. This article presents nonparametric predictive inference (NPI) for selecting the optimal thresholds of a diagnostic test. NPI is a frequentist statistical method that is explicitly aimed at using few modeling assumptions, enabled through the use of lower and upper probabilities to quantify uncertainty. Based on multiple future observations, the NPI approach is presented for selecting the optimal thresholds for two-group and three-group scenarios. In addition, a pairwise approach has also been presented for the three-group scenario. The article ends with an example to illustrate the proposed methods and a simulation study of the predictive performance of the proposed methods along with some classical methods such as Youden index. The NPI-based methods show some interesting results that overcome some of the issues concerning the predictive performance of Youden’s index