Cosmological structure formation with augmented Lagrangian perturbation theory

We present a new fast and efficient approach to model structure formation with augmented Lagrangian perturbation theory (ALPT). Our method is based on splitting the displacement field into a long-and a short-range component. The long-range component is computed by second-order LPT (2LPT). This approximation contains a tidal non-local and non-linear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low-density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zel'dovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius r(S) is used to separate between both regimes. We use the result of 25 dark-matter-only N-body simulations to benchmark at z = 0 the different approximations: first-, second-, third-order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing similar to 25 and similar to 75 per cent higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc(-1), respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with rS = 4-5 h(-1) Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.