Abstract
A forward model of matter and biased tracers at arbitrary order in Lagrangian perturbation theory (LPT) is presented. The forward model contains the complete LPT displacement field at any given order in perturbations, as well as all relevant bias operators at that order and leading order in derivatives. The construction is done for any expansion history and does not rely on the Einstein-de Sitter approximation. A large subset of higher-derivative bias operators is also included. As validation test, we compare the nLPT-predicted matter density field and that from N-body simulations using the same initial conditions. For simulations using a cutoff in the initial conditions, we find subpercent agreement up to scales of k ∼ 0.2 h -1 Mpc. We also find subpercent agreement with full simulations without cutoff, both for the power spectrum and nonlinear σ8-inference, when allowing for the effective sound speed. The application to biased tracers (halos) has already been presented in a recent paper [1].
Highlights
ArXiv ePrint: 2012.09837 expansion for a general expansion history, rather than the Einstein-de Sitter approximation assumed in the published perturbative forward models
The forward model presented here is based on Lagrangian perturbation theory (LPT), which has been studied extensively for matter [4, 21,22,23,24,25,26], and for biased tracers [27, 28]
We have found that their impact on all statistics considered here is very small ( 10−4 − 10−3 depending on the value of the cutoff), significantly smaller at low z than the effect of incorporating the exact ΛCDM expansion history
Summary
Lagrangian perturbation theory starts with the geodesic equation for nonrelativistic matter with initially vanishing peculiar velocity and density perturbation. At a given order n we determine the independent shapes generated by the source terms in Eq (2.10), and integrate the ODE from deep in matter domination, starting with initial conditions αnL,,pT = 0 = αnL,,pT. We have found that their impact on all statistics considered here is very small ( 10−4 − 10−3 depending on the value of the cutoff), significantly smaller at low z than the effect of incorporating the exact ΛCDM expansion history This is because the transverse part of the displacement is always much smaller than the longitudinal part (note that this is a consequence of assuming only scalar initial perturbations, i.e. vanishing initial t). The final result is the Eulerian density field δ(x, τ ) on a grid of size NC3IC at a given time τ , to any desired order in LPT, and for any expansion history. We turn to the construction of the fields appearing in the bias expansion of tracers
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