Displacement Field Analysis via Optimal Transport: Multi-Tracer Approach to Cosmological Reconstruction

We demonstrate the effectiveness of one of the many multi-tracer analyses enabled by Optimal Transport (OT) reconstruction. Leveraging a semi-discrete OT algorithm, we determine the displacements between initial and observed positions of biased tracers and the remaining matter field. With only redshift-space distorted final positions of biased tracers and a simple premise for the remaining mass distribution as input, OT solves the displacement field. This extracted field, assuming asymptotically uniform density and a gradient flow displacement, enables reconstruction of the initial overdensity fluctuation field. We show that the divergence of the OT displacement field is a good proxy of the linear density field, even though the method never assumes the linear theory growth. Additionally, this divergence field can be combined with the reconstructed protohalos to provide a higher signal-to-noise measurement of the BAO standard ruler than was possible with either measurement individually.