The goal of this PhD project is to develop all necessary tools for an efficient and reliable analysis of Euclid weak-lensing and lensing - galaxy cross-correlation data. Starting from the measured Euclid weak-lensing galaxy shapes and spectroscopic galaxy data from Euclid and other surveys such as BOSS, eBOSS, and DESI, the student will construct various estimators of lensing and cross-correlation observables.

Combinations of these observables as function of scale, redshift, and galaxy properties will be optimised to maximally extract cosmological information from the data. In addition, detailed modelling of systematic effects will be carried out to control and minimize their influence on the results.

The student will make use of, and further develop modern statistical inference tools for efficient parameter inference. Theoretical predictions of observables from models of the expansion history and large-scale structure of the Universe will be created in an automatic differentiation framework, e.g. using the library jaxcosmo, exploiting massive parallel computations on GPUs and the ability to compute

gradients of the likelihood to accelerate inference. This will open up efficient (Bayesian) inference methods that make use of the gradients of the models with respect to parameters. Compared to traditional sampling techniques, these methods offer a significant computation time speed-up, and the ability to efficiently explore a large number of parameters. This is important for exploring non-standard models of gravity with additional parameters, and flexible models with many nuisance parameters. It also allows us to include detailed, time-consuming modelling of systematic and higher-order effects.