Fast Gaussian Marginal Neural Posterior Estimation of Cosmological Initial Conditions

Abstract Knowledge of the primordial matter density field from which the large-scale structure of the Universe emerged over cosmic time is of fundamental importance for cosmology. However, reconstructing these cosmological initial conditions from late-time observations is a notoriously difficult task, which requires advanced cosmological simulators and sophisticated statistical methods to explore a multi-million-dimensional parameter space. We show how simulation-based inference (SBI) can be used to tackle this problem and to obtain data-constrained realisations of the primordial dark matter density field in a simulation-efficient way with general non-differentiable simulators. Our method is applicable to full high-resolution dark matter N-body simulations and is based on modelling the posterior distribution of the constrained initial conditions with a Gaussian ansatz whose covariance matrix is diagonal in Fourier space. As a result, we can generate thousands of samples from this approximate posterior within seconds on a single GPU, orders of magnitude faster than existing methods, paving the way for active-learning SBI for cosmological fields. Furthermore, we parameterise the likelihood precision as an isotropic function of wavenumber k, specified by a small set of learned nodes, effectively transforming any point-estimator of initial conditions into a fast sampler. We also study how the learned precision varies with the observational noise level and the size of the training set. We test the validity of our obtained samples by comparing them to the true values with summary statistics and detailed posterior predictive tests, thus determining the range of validity of the Gaussian approximation.