Staying with the Hubble Trouble

This thesis investigates the tension between the expansion rate, also known as the Hubble-Lemaître constant, H0 , measurements by a number of independent early- and late-time observables. In the first part, we consider an alternative to the standard theory of gravity, the generalised Proca (GP) theory, which can potentially alleviate the Hubble tension. Focusing on the GP Lagrangian at cubic order – the Cubic Vector Galilen (CVG) model – we derive the simplified equations for gravity and vector modes and implement them in a modified version of the ECOSMOG N-body code and augmented it further with ray-tracing modules taken from Ray-RAMSES. Accordingly, we conduct the first broad simulation study of a cosmologies based on the CVG theory. They explore the formation, evolution and clustering of dark matter based on matter, halo, weak lensing and voids statistics. In the second part, we attempt to answer whether systematic errors in strong gravitational time delay measurements could partly explain the Hubble tension. We quantify the impact of line-of-sight structures on time-delay measurements and in turn, on the inferred value of H0 , and test the reliability of existing procedures for correcting for these line-of-sight effects. In that pursuit we create realistic lightcones using multiple lens plane ray-tracing to create a set of simulated strong lensing systems that are derived from the CosmoDC2 semi-analytical extra- galactic catalogue.