Field-level cosmological model selection: field-level simulation-based inference for Stage IV cosmic shear can distinguish dynamical dark energy

We present a framework that for the first time allows Bayesian model comparison to be performed for field-level inference of cosmological models. We achieve this by taking a simulation-based inference (SBI) approach using neural likelihood estimation, which we couple with the learned harmonic mean estimator in order to compute the Bayesian evidence for model comparison. We apply our framework to mock Stage IV cosmic shear observations to assess its effectiveness at distinguishing between various models of dark energy. If the recent DESI results that provided exciting hints of dynamical dark energy were indeed the true underlying model, our analysis shows Stage IV cosmic shear surveys could definitively detect dynamical dark energy. We also perform traditional power spectrum likelihood-based inference for comparison, which we find is not able to distinguish between dark energy models, highlighting the enhanced constraining power for model comparison of our field-level SBI approach.