Isobaric Reconstruction of the Baryonic Acoustic Oscillation

In this paper, we report a significant recovery of the linear baryonic acoustic oscillation (BAO) signature by applying the isobaric reconstruction algorithm to the non-linear matter density field. Assuming only the longitudinal component of the displacement being cosmologically relevant, this algorithm iteratively solves the coordinate transform between the Lagrangian and Eulerian frames without requiring any specific knowledge of the dynamics. For dark matter field, it produces the non-linear displacement potential with very high fidelity. The reconstruction error at the pixel level is within a few percent, and is caused only by the emergence of the transverse component after the shell-crossing. As it circumvents the strongest non-linearity of the density evolution, the reconstructed field is well-described by linear theory and immune from the bulk-flow smearing of the BAO signature. Therefore this algorithm could significantly improve the measurement accuracy of the sound horizon scale. For a perfect large-scale structure survey at redshift zero without Poisson or instrumental noise, the fractional error is reduced by a factor of 2.7, very close to the ideal limit with linear power spectrum and Gaussian covariance matrix.