Field-Level Cosmological Inference

Modern cosmological surveys, from cosmic microwave background experiments to optical galaxy surveys, amass data at the petabyte scale. Prior to inference, these data are typically compressed into low-dimensional summary statistics, discarding substantial information, including non-Gaussian features, and complicating multiprobe analyses. I present an emerging opportunity to reimagine cosmological inquiry through field-level inference (FLI). FLI replaces summary statistics with a forward model that directly compares simulated observables to data. This formulation preserves map-level information and naturally unifies map-making, multiprobe combination, and parameter inference, but it leads to high-dimensional, non-Gaussian posteriors whose structure must be understood and controlled. I introduce field-level inference as a practical methodology spanning theory, modeling, and applications. I analyze the mathematical structure of FLI in analytically tractable regimes; extend FLI to weak gravitational lensing with controlled systematics; develop a fast, differentiable forward model that evolves and ray-traces through nonlinear matter structures; and introduce a flexible field-level correction for baryonic feedback effects. I also discuss adjacent topics, including a map-level test of the isotropy of cosmic expansion and the decontamination of atmospheric foregrounds in ground-based CMB data. Collectively, these results demonstrate how the field-level approach can be made accurate, computationally feasible, and robust for cosmological inference.