<scp>emuflow</scp>: normalizing flows for joint cosmological analysis

ABSTRACT Given the growth in the variety and precision of astronomical data sets of interest for cosmology, the best cosmological constraints are invariably obtained by combining data from different experiments. At the likelihood level, one complication in doing so is the need to marginalize over large-dimensional parameter models describing the data of each experiment. These include both the relatively small number of cosmological parameters of interest and a large number of ‘nuisance’ parameters. Sampling over the joint parameter space for multiple experiments can thus become a very computationally expensive operation. This can be significantly simplified if one could sample directly from the marginal cosmological posterior distribution of preceding experiments, depending only on the common set of cosmological parameters. We show that this can be achieved by emulating marginal posterior distributions via normalizing flows. The resulting trained normalizing flow models can be used to efficiently combine cosmological constraints from independent data sets without increasing the dimensionality of the parameter space under study. The method is able to accurately describe the posterior distribution of real cosmological data sets, as well as the joint distribution of different data sets, even when significant tension exists between experiments. The resulting joint constraints can be obtained in a fraction of the time it would take to combine the same data sets at the level of their likelihoods. We construct normalizing flow models for a set of public cosmological data sets of general interests and make them available, together with the software used to train them, and to exploit them in cosmological parameter inference.