Accurate $N$-body simulations with local Primordial non-Gaussianities: initial conditions and aliasing

TL;DR

This work addresses the need for accurate N-body simulations incorporating local primordial non-Gaussianity (PNG) to leverage next-generation galaxy surveys. By systematically varying the starting redshift, LPT order, and PNG amplitudes, the authors show that using 3LPT at a starting redshift around z_ini ≈ 11.5 achieves sub-percent agreement with a high-resolution reference for the power spectrum, bispectrum, and halo mass function, while PNG aliasing at initial conditions remains a sub-percent contributor by z = 0. They quantify PNG aliasing effects, finding initial signals up to ~3% in the power spectrum and up to ~10% in the bispectrum, but these are largely erased by non-linear evolution, and halo bias parameters are largely unaffected. A cross-code comparison of MonofonIC, 2LPTPNG, FastPM, and LPICOLA shows sub-percent consistency for realistic amplitudes of local PNG, with some code-dependent variations due to white-noise realizations, which remain within cosmic variance. Together, these results provide practical, efficient guidelines for generating accurate PNG initial conditions and validating IC generators for upcoming LSS surveys.

Abstract

New generation galaxy surveys targeting constraints on local primordial non-Gaussianity (PNG) demand $N$-body simulations that accurately reproduce its effects. In this work, we explore various prescriptions for the initial conditions of simulations with PNG, aiming to optimise accuracy and minimise numerical errors, particularly due to aliasing. We have used $186$ runs that vary the starting redshift, LPT order, and non-Gaussianities ($f^{\rm local}_{\rm NL}$ and $g^{\rm local}_{\rm NL}$). Starting with $3$LPT at a redshift as low as $z_{\rm ini}\simeq 11.5$ reproduces to $<1 \%$ the power spectrum, bispectrum and halo mass function of a high-resolution reference simulation. The aliasing induced by the PNG terms in the power spectrum produces a $ \leq 3 \%$ excess small-scale power at the initial conditions, dropping below $0.1\%$ by $z=0$. State-of-the-art initial condition generators show a sub-percent agreement. We show that initial conditions for simulations with PNG should be established at a lower redshift using higher-order LPT schemes. We also show that removing the PNG aliasing signal is unnecessary for current simulations. The methodology proposed here can accelerate the generation of simulations with PNG while enhancing their accuracy.

Figures (7)

• Figure 1: Comparison at $z=0$ of the matter power spectrum (upper panels) and bispectrum (lower panels, squeezed limit $(k_1 = k_2 = k;\; k_3=3k_f)$) with respect a high-resolution reference simulation (see \ref{['sec:reference_sims']}). The left panel shows the results for $f_{\rm NL}=0$ simulations, and the right panel for those with $f_{\rm NL} = 100$. The line colour encodes the LPT order used for the initial conditions (red: $1$LPT, green: $2$LPT, and blue: $3$LPT), while the line styles indicate the initial redshift. The shaded regions indicate the $\pm 1\%$ around the reference simulation. The results are nearly identical for $f_{\rm NL} = 0$ and $f_{\rm NL} = 100$. A later start using higher-order LPT schemes improves the agreement with the higher-resolution reference simulations.
• Figure 2: Comparison at $z=0$ of the halo mass function for different configurations of the initial conditions (see \ref{['sec:simulations']}) with respect to the higher-resolution reference simulations (see \ref{['sec:reference_sims']}). The upper panel shows the results for the $f_{\rm NL}=0$ simulations, while the lower panel shows the case with $f_{\rm NL}=100$. The line colour encodes the LPT order used for the initial conditions (red: $1$LPT, green: $2$LPT, and blue: $3$LPT), while the line styles indicate the initial redshift. The dashed vertical lines show the limit of $20$ particles per halo; the limit of $100$ is indicated by the dash-dotted vertical lines. The shaded regions indicate the $1\%$ difference around the reference simulation. Starting the simulation at lower redshifts improves the convergence towards the high-resolution reference.
• Figure 3: Relative difference of the aliased with respect to the de-aliased (see \ref{['sec:aliasing']}) matter power spectrum (left panel) and bispectrum in the squeezed limit $(k_1=k_2= k;\;k_3=k_f )$ (right panel). In the upper panels, we show the differences for initial conditions at $z=24$, and in the lower panels, the results for the final snapshot at $z=0$. The results for simulations with different PNG models are shown in different colours, as indicated in the legend. The shaded areas show the $1\%$ difference around the higher-resolution reference simulation (\ref{['sec:reference_sims']}). Aliasing introduces a spurious signal in the initial conditions (upper panels) for both the power spectrum and bispectrum, reaching $3\%$ and $10 \%$ differences, respectively, in the $g_{\rm NL}=10^{7}$ case. By late times ($z=0$), these discrepancies are suppressed to below $1 \%$ across all scales and PNG parameter values considered.
• Figure 4: Ratio at $z=0$ of the halo mass functions from simulations affected by PNG aliasing to the de-aliased corresponding simulation (see \ref{['sec:aliasing']}). As indicated in the legend, the line colours correspond to the different PNG models used in the simulations. The shaded area represents the $1\%$ variation around the de-aliased simulations. The PNG aliasing signal produces variations below $3\%$ in the halo mass function at $z=0$.
• Figure 5: Measurements at $z=0$ of the linear bias parameter $b_1$ (upper panel) and the PNG-response parameter $p$ (lower panel) for halos from the simulations summarised in \ref{['tab:simulations']}. The colours indicate the LPT order used for the initial conditions (red: $1$LPT, green: $2$LPT, and blue: $3$LPT). The crosses present the best-fit values with the $1\sigma$ error bars from the fits for the simulations with a PNG aliasing signal. The circles present the results after removing the PNG alias signal, or de-aliased simulations (see \ref{['sec:aliasing']}). The horizontal grey lines show the measurements from our reference high resolution simulations (see \ref{['sec:reference_sims']}). The grey regions show the $1\sigma$ uncertainty from the fit to the reference simulation (\ref{['sec:reference_sims']}). In the lower panel, the dashed horizontal line shows the universality relation, $p=1$.