  Optimal transport theory has recently reemerged as a vastly resourceful field
of mathematics with elegant applications across physics and computer science.
Harnessing methods from geometry processing, we report on the efficient
implementation for a specific problem in cosmology -- the reconstruction of the
linear density field from low redshifts, in particular the recovery of the
Baryonic Acoustic Oscillation (BAO) scale. We demonstrate our algorithm's
accuracy by retrieving the BAO scale in noise-less cosmological simulations
that are dedicated to cancel cosmic variance; we find uncertainties to be
reduced by a factor of 4.3 compared with performing no reconstruction, and a
factor of 3.1 compared with standard reconstruction.
