Nonlinear reconstruction

Abstract

We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (r δr δ L > 0.5 for k 1 h/Mpc) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping initiatives.

New method for initial density reconstruction

“…[28,32], as we show below, it succeeds in recovering the initial density field to the same accuracy as the other methods, which suggests that these methods all face the same limitation: after shell crossing it is no longer possible to uniquely find a particle's Lagrangian position. Our test shows that, despite this limitation, the method can greatly improve the reconstruction of BAO peaks in real space.…”

“…Reconstruction in the context of cosmology has been visited by various groups that utilize different techniques, for example, [16,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] (see Refs. [30,32] for detailed historical reviews).…”

“…Reference [16] proposed a simple reconstruction based on Zel'dovich approximation that can sharpen the BAO peak and thus improve the BAO measurement accuracy, which has been demonstrated in real observations [4,36,37]. This has motivated many studies of alternative methods of improving the BAO signal (e.g., [28,32,38,39]). Reconstructing the initial conditions helps to reduce the damping of the BAO peaks caused by nonlinear evolution, which, for example, Ref.…”

“…Recently proposed iterative methods such as [28,32] managed to push the scale where linear density information can be reliably recovered to k ∼ 0.5-0.6 h=Mpc, which can lead to a substantial reduction of the uncertainty in BAO measurement [30,32]. However, given the importance of the BAO reconstruction problem, and that different methods could have different limitations, it will be highly beneficial to develop independent methods that have their own merits.…”

“…This algorithm is similar in spirit to the Newton-Ralpson algorithm to solve nonlinear algebraic equations: one starts from an initial guess of the solution, and then iteratively improves the guess until the trial solution is close enough to the true solution. This iterative nature of our method, however, is different from the iterations of other methods, e.g., [28,32], in that we do not displace particles in each iteration step, and the iteration here is purely a numerical tool for solution finding. We can move particles to their Lagrangian positions once the solution to the PDE is obtained, although this is unnecessary if we are only interested in having the initial density field.…”