The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

Galaxy cluster cosmology in KiDS, Planck, and Euclid surveys

In this Thesis, we present a series of works that encompass the fundamental steps of cosmological analyses based on galaxy clusters, spanning from mass calibration to deriving cosmological constraints through counts and clustering. Firstly, we focus on the 3D two-point correlation function (2PCF) of the galaxy cluster sample by Planck Collaboration XXVII (2016). The masses of these clusters are expected to be underestimated, as they are derived from a scaling relation calibrated through X-ray observations. We derived a mass bias which disagrees with simulation predictions, consistent with what derived by Planck Collaboration VI (2020). Furthermore, in this Thesis we analyse the cluster counts and 2PCF, respectively, of the photometric galaxy cluster sample developed by Maturi et al. (2019), based on the third data release of KiDS (KiDS-DR3, de Jong et al. 2017). We derived constraints on fundamental cosmological parameters which are consistent and competitive, in terms of uncertainties, with other state-of-the-art cosmological analyses. Then, we introduce a novel approach to establish galaxy colour-redshift relations for cluster weak-lensing analyses, regardless of the specific photometric bands in use. This method optimises the selection completeness of cluster background galaxies while maintaining a defined purity threshold. Based on the galaxy sample by Bisigello et al. (2020), we calibrated two colour selections, one relying on the ground-based griz bands, and the other including the griz and Euclid YJH bands. In addition, we present the preliminary work on the weak-lensing mass calibration of the clusters detected by Maturi et al. (in prep.) in the fourth data release of KiDS (KiDS-1000, Kuijken et al. 2019). This mass calibration will enable the cosmological analyses based on cluster counts and clustering, from which we expect remarkable improvements in the results compared to those derived in KiDS-DR3.