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Galaxy clusters are tracers of the growth of structures and the expansion of the Universe. Measuring their abundance enables us to investigate the nature of dark energy and dark matter, making them one of the primary cosmological probes to be used in future galaxy surveys.
The relation between cluster masses and the number of galaxies they contain, known as the scaling relation, is a key factor for the cosmological use of cluster counts in the optical. However, this relation remains one of the limiting factors in current analyses because cluster masses are not directly observable. Nevertheless, they can be estimated through the gravitational lensing effect, where light from background sources is deflected by the cluster gravitational fields. As a result, the observed galaxy images undergo a coherent distortion, allowing for the reconstruction of their mass distribution. This thesis focuses on various aspects of cosmological inference using cluster lensing and abundance in the era of large-scale cosmological surveys such as the Rubin LSST.
A central part of this work was performed as part of the LSST Dark Energy Science Collaboration (DESC), which focuses on the cosmological analyses using LSST data. I joined the DESC effort by contributing to the development of software tools for cluster lensing and cluster abundance analyses, using DESC simulated datasets. These datasets contain ideal and realistic LSST-like galaxy catalogs, the validation of which I contributed to. Furthermore, using the several codes I developed, I derived preliminary cosmological constraints from the cluster abundance in the DESC simulations. I also focused on the impact of the several systematic effects on the weak lensing mass reconstruction and how these propagate to the cosmological constraints.
Galaxy cluster triaxial morphology and resulting projection effects can yield biases on the mass reconstruction. Valuable information on cluster morphology can be extracted from the multipoles of the local shear and releasing the spherical symmetry assumption that is generally made. As part of the cluster simulation project The Three Hundred, I developed an analysis based on lensing shear multipoles to gain insights on the triaxial properties of the cluster mass distribution and check whether this could improve the lensing mass calibration. From this work, I found that including multipole moments of the local shear permits reconstructing the ellipticity and orientation of the projected mass distribution. However, gain on the mass reconstruction remains marginal and a strong degeneracy exists between the lensing mass estimate and elongation/flattening parameter for triaxial clusters whose major axes are aligned along the line-of-sight.
One of the key ingredients to constrain cosmology is the likelihood function, that describes the statistical properties of the observed cluster counts in bins of cluster redshift and cluster mass. I developed a methodology to test the accuracy and robustness of cluster abundance binned likelihoods that are widely used in the literature (Poisson, the Gaussian and the Gauss-Poisson Compound likelihood (GPC)) and applied it to the 1000 PINOCCHIO simulated dark matter halo catalogs. The main finding is that for a variety of cosmological inference setups, the Poisson likelihood underestimates errors by 20-30%, whereas the Gaussian and GPC give similar and robust errors for LSST or Euclid-like surveys.
In addition, I have also developed a new unbinned cluster count formalism allowing us to account for the effect of Super-Sample Covariance, which is an inherent source of scatter for large scale structure observables such as galaxy clusters. The resulting cosmological constraints are stronger than in the binned approach but only slightly differ from the more standard unbinned method.