Optimal Transport Reconstruction of Baryon Acoustic Oscillations

A weighted, semidiscrete, fast optimal transport (OT) algorithm for reconstructing the Lagrangian positions of protohalos from their evolved Eulerian positions is presented. The algorithm makes use of a mass estimate of the biased tracers and of the distribution of the remaining mass (the dust) but is robust to errors in the mass estimates. Tests with state-of-art cosmological simulations show that if the dust is assumed to have a uniform spatial distribution, then the shape of the OT-reconstructed pair correlation function of the tracers is very close to linear theory, enabling subpercent precision in the baryon acoustic oscillation distance scale that depends weakly, if at all, on a cosmological model. With a more sophisticated model for the dust, OT returns an estimate of the displacement field which yields superb reconstruction of the protohalo positions and, hence, of the shape and amplitude of the initial pair correlation function of the tracers. This enables direct and independent determinations of the bias factor b and the smearing scale Sigma, potentially providing new methods for breaking the degeneracy between b and sigma(8).

Automated summary

This study presents a fast optimal transport algorithm for reconstructing the Lagrangian positions of protohalos from their evolved Eulerian positions. It can handle errors in mass estimates and achieve subpercent precision in measuring the baryon acoustic oscillation distance scale. By using a more sophisticated dust model, it can estimate the displacement field accurately and provide new methods for determining the bias factor and smearing scale.