Fast numerical method to generate halo catalogues in modified gravity (part I): second-order Lagrangian perturbation theory. Issue 1 (3rd February 2020) - Moretti, C; Mozzon, S; Monaco, P; Munari, E; Baldi, M
ABSTRACT: We present a new numerical method to determine second-order Lagrangian displacement fields in presence of modified gravity (MG). We start from the extension of Lagrangian perturbation theory (LPT) to a class of MG models, which can be described by a parametrized Poisson equation. We exploit Fast Fourier transforms to compute the full source term of the differential equation for the second-order Lagrangian displacement field. We compare its mean to the source term computed for specific configurations, for which a k -dependent solution can be found numerically. We choose the configuration that best matches the full source term, thus obtaining an approximate factorization of the second-order displacement field as the space term valid for Λ Cold Dark Matter (ΛCDM) times a k -dependent, second-order growth factor. Such approximation is used to compute second-order displacements for particles. The method is tested against N -body simulations run with standard and f ( R ) gravity: we rely on the results of a friends-of-friends code run on the N -body snapshots to assign particles to haloes, then compute the halo power spectrum. We find very consistent results for the two gravity theories: second-order LPT (2LPT) allows to recover the N -body halo power spectrum within ∼10 per cent precision to k  ∼ 0.2–0.4  h  Mpc −1, as well as halo positions. We show that the performance of 2LPT with MG is the same (within 1 per cent) as the one obtained for standard ΛCDM case. This formulation of 2LPT can quickly generate dark matter distributions with f ( R ) gravity, and can easily be extended to other MG theories.