Field-based physical inference from peculiar velocity tracers

Abstract

ABSTRACT We present a proof-of-concept Bayesian hierarchical modelling approach to reconstruct the initial cosmic matter density field constrained by peculiar velocity observations. Using a model for the gravitational evolution of dark matter to connect the initial conditions to late-time observations, it reconstructs the late-time density and velocity fields as natural byproducts. We implement this field-based physical inference approach by adapting the Bayesian Origin Reconstruction from Galaxies ($\small {\rm BORG}$) algorithm, which explores the high-dimensional posterior through the use of Hamiltonian Monte Carlo sampling. We test the self-consistency of the method using random sets of tracers, and assess its accuracy in a more complex scenario where peculiar velocity tracers are mock haloes drawn from $\small {\rm GADGET2}$ N-body simulations. We find that our framework self-consistently infers the initial conditions, density and velocity fields, and shows some robustness to model mis-specification. Compared with the approach of constrained Gaussian random fields/Wiener filtering, the hierarchical model produces more accurate final density and velocity field reconstructions. It also allows us to constrain the initial conditions by peculiar velocity observations, complementing in this aspect other field-based approaches based on alternative cosmological observables such as galaxy clustering or weak lensing.