Modern cosmology is strongly data-driven. Theoretical predictions are compared to surveys through forward models, selection functions, window functions, nuisance parameters, and hierarchical Bayesian inference.

Boltzmann codes solve the linearized Einstein-Boltzmann system for CMB and matter transfer functions, while $N$-body and hydrodynamic simulations model nonlinear evolution. Emulators and machine learning surrogate models are increasingly used to accelerate parameter scans.

Parameter posteriors are obtained from $$P(\theta|d) \propto P(d|\theta)P(\theta).$$ Cosmological analyses must account for non-Gaussian likelihoods, degeneracies, covariances, and systematic errors such as photometric calibration, intrinsic alignments, and redshift uncertainty.

As statistical errors shrink, systematics dominate. Examples include shear calibration, blending, baryonic feedback, intrinsic alignments, redshift-space distortions, foreground contamination, and selection bias. Robust inference requires nuisance marginalization and cross-validation between probes.

Major open problems include the nature of dark matter, the microphysics of inflation and reheating, the origin of baryon asymmetry, the cosmological constant problem, tensions between local and early-universe determinations of $H_0$, and possible hints of new physics in structure growth.