Accurate Baryon Acoustic Oscillations Reconstruction via Semidiscrete Optimal Transport

Optimal transport theory has recently re-emerged 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 noiseless 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.

Figure 1

Semidiscrete Monge-Ampére-Kantorovich reconstruction. Illustration of the reconstruction’s flow beginning with an input of point masses at ${\tau }_F$ (here $z=0$) that are mapped to their corresponding regions at ${\tau }_I$ (here $z\to \infty$) from where they draw their mass through gravitational collapse. The regions are the polyhedral cells defined by the Laguerre diagram as defined in the main body. In a subsequent step the cells evolve until a time ${\tau }_F>\tau >{\tau }_I$ (here $z=9$) and according to a LPT description—in the present Letter the Zel’dovich approximation. In the final step a mass density is expressed on a Eulerian mesh. The figure shows a tiny subset of a reconstruction from AbacusCosmos, that comprises $9.7\times {10}^6$ Laguerre cells.

Figure 2

Fractional BAO signal in simulations and reconstructions. Top panel: ratio of power spectra from simulations with and without BAO signal, averaged over ten FastPM simulations and their reconstructions, $⟨P_{\mathrm{wig}}(k)-P_{\mathrm{nw}}(k)⟩/⟨P_{\mathrm{wig}}(k)⟩$. Bottom panel: deviations from the initial condition’s fractional BAO signal, ${\mathrm{\Delta }}^{\mathrm{IC}}(k)=⟨P_{\mathrm{wig}}(k)⟩/⟨P_{\mathrm{nw}}(k)⟩-⟨P_{\mathrm{wig}}^{\mathrm{IC}}(k)⟩/⟨P_{\mathrm{nw}}^{\mathrm{IC}}(k)⟩$. The shaded band indicates the standard deviation ${\sigma }^{\mathrm{IC}}(k)$ as estimated from the simulations and defined in the text.