Hamiltonian Monte Carlo reconstruction from peculiar velocities

ABSTRACT The problem of the reconstruction of the large-scale density and velocity fields from peculiar velocity surveys is addressed here within a Bayesian framework by means of Hamiltonian Monte Carlo (HMC) sampling. The HAmiltonian Monte carlo reconstruction of the Local EnvironmenT (hamlet) algorithm is designed to reconstruct the linear large-scale density and velocity fields in conjunction with the undoing of lognormal bias in the derived distances and velocities of peculiar velocity surveys, such as the Cosmicflows (CF) data. The hamlet code has been tested against CF mock catalogues consisting of up to 3 × 104 data points with mock errors akin to those of the Cosmicflows-3 (CF3) data, within the framework of the Lambda cold dark matter standard model of cosmology. The hamlet code outperforms previous applications of Gibbs sampling Markov chain Monte Carlo reconstruction from the CF3 data by two to four orders of magnitude in CPU time. The gain in performance is due to the inherent higher efficiency of the HMC algorithm and due to parallel computing on GPUs rather than CPUs. This gain will enable an increase in the reconstruction of the large-scale structure from the upcoming CF4 data and the setting of constrained initial conditions for cosmological high-resolution simulations.