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Register a new userAnalysis of two-point statistics of cosmic shear: III. Covariances of shear measures made easy
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In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear statistics have been developed in order to analyze data from surveys. For the covariances of the prevalent second-order measures we present simple and handy formulae, valid under the assumptions of Gaussian density fluctuations and a simple survey geometry. We also formulate these results in the context of shear tomography, i.e. the inclusion of redshift information, and generalize them to arbitrary data field geometries. We define estimators for the E- and B-mode projected power spectra and show them to be unbiased in the case of Gaussianity and a simple survey geometry. From the covariance of these estimators we demonstrate how to derive covariances of arbitrary combinations of second-order cosmic shear measures. We then recalculate the power spectrum covariance for general survey geometries and examine the bias thereby introduced on the estimators for exemplary configurations. Our results for the covariances are considerably simpler than and analytically shown to be equivalent to the real-space approach presented in the first paper of this series. We find good agreement with other numerical evaluations and confirm the general properties of the covariance matrices. The studies of the specific survey configurations suggest that our simplified covariances may be employed for realistic survey geometries to good approximation.
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We introduce an optimized data vector of cosmic shear measures (N). This data vector has high information content, is not sensitive against B-mode contamination and only shows small correlation between data points of different angular scales. We show that a data vector of the two-point correlation function (2PCF) in general contains more information on cosmological parameters compared to a data vector of the aperture mass dispersion. Reason for this is the fact that <M_ap^2> lacks the information of the convergence power spectrum (P_kappa) on large angular scales, which is contained in the 2PCF data vector. Therefore we create a combined data vector N, which retains the advantages of <M_ap^2> and in addition is also sensitive to the large-scale information of P_kappa. We compare the information content of the three data vectors by performing a detailed likelihood analysis and use ray-tracing simulations to derive the covariance matrices. In the last part of the paper we contaminate all data vectors with B-modes on small angular scales and examine their robustness against this contamination.The combined data vector strongly improves constraints on cosmological parameters compared to <M_ap^2>. Although, in case of a pure E-mode signal the information content of the 2PCF is higher, in the more realistic case where B-modes are present the 2PCF data vector is strongly contaminated and yields biased cosmological parameter estimates. N shows to be robust against this contamination. Furthermore the individual data points of N show a much smaller correlation compared to the 2PCF leading to an almost diagonal covariance matrix.
We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), doubling the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat $Lambda$CDM model, we find $S_8 = sigma_8 (Omega_{rm m}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021}$ for our fiducial analysis, which is in $3sigma$ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary analyses of the two-point shear correlation function and band power spectra, finding results to be in excellent agreement. We investigate the sensitivity of all three statistics to a number of measurement, astrophysical, and modelling systematics, finding our $S_8$ constraints to be robust and dominated by statistical errors. Our cosmological analysis of different divisions of the data pass the Bayesian internal consistency tests, with the exception of the second tomographic bin. As this bin encompasses low redshift galaxies, carrying insignificant levels of cosmological information, we find that our results are unchanged by the inclusion or exclusion of this sample.
We explore the stability of the variance and skewness of the cosmic gravitational convergence field, using two different approaches: first we simulate a whole MEGACAM survey (100 sq. degrees). The reconstructed mass map, obtained from a shear map, shows that the state-of-the-art data analysis methods can measure weak-lensing statistics at angular scales ranging from 2.5 to 25. We looked also at the influence of a varying signal-to-noise ratio over the shear map (due to local variations of source density) on the mass reconstruction, by means of Monte-Carlo simulation. The effect at small scales can easily be corrected-for in most of the relevant cases. These results enhance the confidence in the capability of future large surveys to measure accurately cosmologically interesting quantities.
We constrain cosmological parameters from a joint cosmic shear analysis of peak-counts and the two-point shear correlation functions, as measured from the Dark Energy Survey (DES-Y1). We find the structure growth parameter $S_8equiv sigma_8sqrt{Omega_{rm m}/0.3} = 0.766^{+0.033}_{-0.038}$, which at 4.8% precision, provides one of the tightest constraints on $S_8$ from the DES-Y1 weak lensing data. In our simulation-based method we determine the expected DES-Y1 peak-count signal for a range of cosmologies sampled in four $w$CDM parameters ($Omega_{rm m}$, $sigma_8$, $h$, $w_0$). We also determine the joint covariance matrix with over 1000 realisations at our fiducial cosmology. With mock DES-Y1 data we calibrate the impact of photometric redshift and shear calibration uncertainty on the peak-count, marginalising over these uncertainties in our cosmological analysis. Using dedicated training samples we show that our measurements are unaffected by mass resolution limits in the simulation, and that our constraints are robust against uncertainty in the effect of baryon feedback. Accurate modelling for the impact of intrinsic alignments on the tomographic peak-count remains a challenge, currently limiting our exploitation of cross-correlated peak counts between high and low redshift bins. We demonstrate that once calibrated, a fully tomographic joint peak-count and correlation functions analysis has the potential to reach a 3% precision on $S_8$ for DES-Y1. Our methodology can be adopted to model any statistic that is sensitive to the non-Gaussian information encoded in the shear field. In order to accelerate the development of these beyond-two-point cosmic shear studies, our simulations are made available to the community upon request.
Following the detection of a cosmic shear signal at the 30 scale using archival parallel data from the STIS CCD camera onboard HST in Haemmerle et al. (2002), we analyzed a larger data set obtained from an HST GO pure parallel program. Although this data set is considerably larger than the one analyzed previously, we do not obtain a significant detection of the cosmic shear signal. The potential causes of this null result are the multiple systematics that plague the STIS CCD data, and in particular the degradation of the CCD charge transfer efficiency after 4 years in space.
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