Optimal Transport Reconstruction of Baryon Acoustic Oscillations
  A model-independent, weighted semi-discrete, fast optimal transport algorithm
to reconstruct the Lagrangian positions of proto-halos from their evolved
Eulerian positions is presented. Tests with state-of-art cosmological
simulations show that the positions of proto-halos are reconstructed
accurately, without having to assume a background cosmology. The algorithm,
which makes use of a mass estimate of the biased tracers, but is robust to
errors in this estimation, recovers the shape and amplitude of the initial pair
correlation function of the tracers, enabling sub-percent precision in the BAO
distance scale that is not tied to a cosmological model. In principle, our
algorithm also allows direct and independent determinations of the bias factor
and the smearing scale, potentially providing new methods for breaking the
degeneracy between the bias factor $b$ and $\sigma_8$.
