Physical Bayesian modelling of the non-linear matter distribution: new insights into the Nearby Universe

Accurate analyses of present and next-generation galaxy surveys require new ways to handle effects of non-linear gravitational structure formation in data. To address these needs we present an extension of our previously developed algorithm for Bayesian Origin Reconstruction from Galaxies to analyse matter clustering at non-linear scales in observations. This is achieved by incorporating a numerical particle mesh model of structure formation into our Bayesian inference framework. The algorithm simultaneously infers the 3D primordial matter fluctuations from which present non-linear observations formed and provides reconstructions of velocity fields and structure formation histories. The physical forward modelling approach automatically accounts for non-Gaussian features in evolved matter density fields and addresses the redshift space distortion problem associated with peculiar motions of galaxies. Our algorithm employs a hierarchical Bayes approach to jointly account for observational effects, such as galaxy biases, selection effects, and noise. Corresponding parameters are marginalized out via a sophisticated Markov Chain Monte Carlo approach relying on a combination of a multiple block sampling framework and a Hamiltonian Monte Carlo sampler. We demonstrate the performance of the method by applying it to the 2M++ galaxy compilation, tracing the matter distribution of the Nearby Universe. We show accurate and detailed inferences of the 3D non-linear dark matter distribution of the Nearby Universe. As exemplified in the case of the Coma cluster, we provide mass estimates that are compatible with those obtained from weak lensing and X-ray observations. For the first time, we reconstruct the vorticity of the non-linear velocity field from observations. In summary, our method provides plausible and detailed inferences of dark matter and velocity fields of our cosmic neighbourhood.