Motivated by recent developments in perturbative calculations of the nonlinear evolution of large-scale structure, we present an iterative algorithm to reconstruct the initial conditions in a given volume starting from the dark matter distribution in real space. In our algorithm, objects are first moved back iteratively along estimated potential gradients, with a progressively reduced smoothing scale, until a nearly uniform catalog is obtained. The linear initial density is then estimated as the divergence of the cumulative displacement, with an optional second-order correction. This algorithm should undo nonlinear effects up to one-loop order, including the higher-order infrared resummation piece. We test the method using dark matter simulations in real space. At redshift $z=0$, we find that after eight iterations the reconstructed density is more than 95% correlated with the initial density at $k\le 0.35h{\mathrm{Mpc}}^{-1}$. The reconstruction also reduces the power in the difference between reconstructed and initial fields by more than 2 orders of magnitude at $k\le 0.2h{\mathrm{Mpc}}^{-1}$, and it extends the range of scales where the full broadband shape of the power spectrum matches linear theory by a factor of 2–3. As a specific application, we consider measurements of the baryonic acoustic oscillation (BAO) scale that can be improved by reducing the degradation effects of large-scale flows. In our idealized dark matter simulations, the method improves the BAO signal-to-noise ratio by a factor of 2.7 at $z=0$ and by a factor of 2.5 at $z=0.6$, improving standard BAO reconstruction by 70% at $z=0$ and 30% at $z=0.6$, and matching the optimal BAO signal and signal-to-noise ratio of the linear density in the same volume. For BAO, the iterative nature of the reconstruction is the most important aspect.

• Received 24 April 2017

DOI:https://doi.org/10.1103/PhysRevD.96.023505