Density split statistic in cosmic shear surveys: Generalisations and its application to the Kilo Degree Survey

Abstract

Understanding the formation and evolution of the Universe’s large-scale structure are fundamental in modern cosmology. Currently, the most accurate model to describe the LSS and other observations like the cosmic microwave background (CMB) is the so-called &Lambda; Cold Dark Matter model (&Lambda;CDM), which is therefore considered the standard model of cosmology. <br /> An ideal tool to measure the total matter distribution in the Universe is gravitational lensing, which describes how massive objects, regardless of the matter’s nature, bend light rays and distort the images of distant objects. <br /> To extract the non-Gaussian information, Gruen et al. (2016) introduced the density split statistic (DSS). The DSS measures the mean tangential shear around line-of-sights of similar galaxy densities. Since the galaxy densities trace the matter densities, the tangential shear correlates strongly with the galaxy distribution in a manner that varies with cosmology. Therefore, the DSS captures information from the number of foreground galaxies in each density bin and the shape and amplitude of the shear profiles. <br /> In the first part of this thesis, we construct a general filter function, which is used to smooth the galaxy density field. The filter function is adapted to the shear pattern. We find that the adapted filter yields a better correlation between the total matter and the galaxy distribution and a larger signal-to-noise ratio than the previously used top-hat filter function. The latter eases the detection of the shear signals compared to the previously used top-hat filter functions making them more suitable for real data analyses. <br /> In the second part, we modify the analytical DSS model described in Friedrich et al. (2018) to general filter functions. Similar to the previous DSS model, we build on log-normal approximations of large deviation theory approaches to model the matter density probability distribution function and on perturbative calculations of higher-order moments of the density field. <br /> In the third part, we validate the modified DSS model against several simulations. This validation reveals that the analytical model is accurate for stage III surveys like the fourth data release of the Kilo-Degree Survey (KiDS-1000). Furthermore, we find that the model is robust against baryonic feedback and intrinsic alignment. <br /> In the last part, we perform a cosmological analysis of KiDS-1000 based on the DSS. The image shapes are taken from the fourth and fifth tomographic bin of KiDS-1000, and the foreground galaxy sample is constructed from a bright galaxy sample. After marginalising over the photometric redshift uncertainty and the residual shear calibration bias, we measure a structure growth parameter of S₈ &equiv; &sigma;₈&radic;&Omega;_m/0.3 &equiv; 0.74^+0.03_-0.02 that is competitive too and consistent with two-point cosmic shear results, a matter density of &Omega;_m = 0.27 &plusmn; 0.02, and a constant galaxy bias of <em>b</em> = 1.32^+0.12_-0.11. <br /> In conclusion, although higher-order statistics are complicated to model and usually rely on cosmological simulations, we show that the generalised model of the DSS is a powerful cosmological tool with a significant advantage in breaking the &Omega;_m-&sigma;₈ degeneracy.