Normalising Flow for Joint Cosmological Analysis

We develop a method to learn the joint posterior of cosmological parameters using MCMC chains from various experiments by leveraging normalising flow to learn the density of each chain. These models are quick to train and, once stored, allow efficient sampling of joint posteriors from any experiment combination. Applied to test cases in cosmology, the method reveals robust accuracy and precision, even when known tensions in parameters like $\sigma_{8}$ exist. The flow model can also be used as a prior in likelihood analyses, significantly speeding up inference by eliminating the need for repeated computationally intensive analyses. Sampling the joint posterior using pre-trained models takes about 15 minutes, making this method highly efficient for cosmological studies.