N-body simulations are key to cosmology but are computationally expensive. ML can speed them up, but can we trust the results? We propose a new method of combining ML and simulations (COmoving Computer Acceleration - COCA) which can catch mistakes made by ML and correct for them.

The strongest tension within the concordance model of cosmology is a mismatch between the Universe's expansion rate inferred from the cosmic microwave background vs the local distance ladder. We construct a Bayesian hierarchical model to infer this rate locally but without requiring supernovae. We still find a significant "Hubble tension", and achieve unprecedented precision by using BORG velocity fields.

BORG is designed for local large-scale structure, but it has significant potential for CMB studies as well. We develop a framework for connecting constrained simulations to the thermal Sunyaez-Zel'dovich effect in the CMB, and use it to show the superiority of BORG relative to other methods and create a new calibration of the cluster mass-observable relation.