Simulation-based inference for cosmology

Modern cosmology has entered a data-rich era, driven by the rapidly growing volume and complexity of increasingly precise and heterogeneous observations, ranging from high-redshift galaxy surveys to detailed measurements of the cosmic microwave background. These observations enable unprecedented tests of cosmological models, but they also expose growing limitations of traditional inference pipelines: explicit likelihood modelling becomes increasingly infeasible in realistic settings, while reducing the data to a limited set of hand-crafted summary statistics can leave a substantial fraction of the available information unused. This thesis explores two complementary avenues for addressing these challenges. First, simulation-based inference (SBI) enables Bayesian inference without requiring an explicit likelihood in settings where only a stochastic simulator of the data is available; second, field-level inference (FLI) works directly with high-dimensional physical fields, allowing their reconstruction while retaining more of the information contained in the full field. We first review the current state of cosmology, the main data analysis methods used in the field, and the challenges they face. We then demonstrate the performance of field-level SBI on the problem of probabilistic reconstruction of the primordial dark matter field by developing a fast method for approximating the field-level posterior for arbitrary non-differentiable simulators. Finally, we apply SBI to cosmological parameter inference for mock Euclid survey data and introduce a framework for directly combining SBI with likelihood-based analyses. Together, these results highlight the potential of SBI and FLI as scalable tools for next-generation cosmological inference.