Conditions For Cosmological N-body Simulations Research Articles

GenetIC—A New Initial Conditions Generator to Support Genetically Modified Zoom Simulations

Abstract We present genetIC, a new code for generating initial conditions for cosmological N-body simulations. The code allows precise, user-specified alterations to be made to arbitrary regions of the simulation (while maintaining consistency with the statistical ensemble). These “genetic modifications” allow, for example, the history, mass, or environment of a target halo to be altered in order to study the effect on their evolution. The code natively supports initial conditions with nested zoom regions at progressively increasing resolution. Modifications in the high-resolution region must propagate self-consistently onto the lower-resolution grids; to enable this while maintaining a small memory footprint, we introduce a Fourier-space filtering approach to generating fields at variable resolution. Due to a close correspondence with modifications, constrained initial conditions can also be produced by genetIC (for example, with the aim of matching structures in the local universe). We test the accuracy of modifications performed within zoom initial conditions. The code achieves subpercent precision, which is easily sufficient for current applications in galaxy formation.

Accurate initial conditions for cosmological N-body simulations: minimizing truncation and discreteness errors

ABSTRACT Inaccuracies in the initial conditions for cosmological N-body simulations could easily be the largest source of systematic error in predicting the non-linear large-scale structure. From the theory side, initial conditions are usually provided by using low-order truncations of the displacement field from Lagrangian perturbation theory, with the first- and second-order approximations being the most common ones. Here, we investigate the improvement brought by using initial conditions based on third-order Lagrangian perturbation theory (3LPT). We show that with 3LPT, truncation errors are vastly suppressed, thereby opening the portal to initializing simulations accurately as late as z = 12 (for the resolution we consider). We analyse the competing effects of perturbative truncation and particle discreteness on various summary statistics. Discreteness errors are essentially decaying modes and thus get strongly amplified for earlier initialization times. We show that late starting times with 3LPT provide the most accurate configuration, which we find to coincide with the continuum fluid limit within 1 per cent for the power- and bispectrum at z = 0 up to the particle Nyquist wavenumber of our simulations (k ∼ 3h Mpc−1). In conclusion, to suppress non-fluid artefacts, we recommend initializing simulations as late as possible with 3LPT. We make our 3LPT initial condition generator publicly available.

Impacts of pre-initial conditions on anisotropic separate universe simulations: a boosted tidal response in the epoch of reionization

ABSTRACT To generate initial conditions for cosmological N-body simulations, one needs to prepare a uniform distribution of simulation particles, the so-called pre-initial condition (pre-IC). The standard method to construct the pre-IC is to place the particles on the lattice grids evenly spaced in the three-dimensional spatial coordinates. However, even after the initial displacement of each particle according to cosmological perturbations, the particle distribution remains to display an artificial anisotropy. Such an artefact causes systematic effects in simulations at later time until the evolved particle distribution sufficiently erases the initial anisotropy. In this paper, we study the impacts of the pre-IC on the anisotropic separate universe simulation, where the effect of large-scale tidal field on structure formation is taken into account using the anisotropic expansion in a local background (simulation volume). To quantify the impacts, we compare the simulations employing the standard grid pre-IC and the glass one, where the latter is supposed to suppress the initial anisotropy. We show that the artificial features in the grid pre-IC simulations are seen until z ∼ 9, while the glass pre-IC simulations appear to be stable and accurate over the range of scales we study. From these results we find that a coupling of the large-scale tidal field with matter clustering is enhanced compared to the leading-order prediction of perturbation theory in the quasi-non-linear regime in the redshift range 5 ≲ z ≲ 15, indicating the importance of tidal field on structure formation at such high redshifts, e.g. during the epoch of reionization.

Suitable initial conditions for Newtonian simulations with massive neutrinos

Initial conditions for cosmological N-body simulations are usually calculated by rescaling the present day linear power spectrum obtained from an Einstein-Boltzmann solver to the initial time employing the scale-independent matter growth function. For the baseline ΛCDM model, this has been shown to be consistent with General Relativity (GR) even in the presence of relativistic species such as photons. We show that this approach becomes significantly more complex in cosmologies with massive neutrinos and present an alternative method based on the Newtonian motion gauge framework.

An alternative method to generate pre-initial conditions for cosmological N-body simulations

Currently, grid and glass methods are the two most popular choices to generate uniform particle distributions (i.e., pre-initial conditions) for cosmological $N$-body simulations. In this article, we introduce an alternative method called the capacity constrained Voronoi tessellation (CCVT), which originates from computer graphics. As a geometrical equilibrium state, a CCVT particle configuration satisfies two constraints: (i) the volume of the Voronoi cell associated with each particle is equal; (ii) every particle is in the center-of-mass position of its Voronoi cell. We show that the CCVT configuration is uniform and isotropic, follows perfectly the minimal power spectrum, $P(k)\propto k^4$, and is quite stable under gravitational interactions. It is natural to incorporate periodic boundary conditions during CCVT making, therefore, we can obtain a larger CCVT by tiling with a small periodic CCVT. When applying the CCVT pre-initial condition to cosmological $N$-body simulations, we show that it plays as good as grid and glass schemes. The CCVT method will be helpful in studying the numerical convergence of pre-initial conditions in cosmological simulations. It can also be used to set up pre-initial conditions in smoothed-particle hydrodynamics simulations.

Initial conditions for accurateN-body simulations of massive neutrino cosmologies

The set-up of the initial conditions in cosmological N-body simulations is usually implemented by rescaling the desired low-redshift linear power spectrum to the required starting redshift consistently with the Newtonian evolution of the simulation. The implementation of this practical solution requires more care in the context of massive neutrino cosmologies, mainly because of the non-trivial scale-dependence of the linear growth that characterises these models. In this work we consider a simple two-fluid, Newtonian approximation for cold dark matter and massive neutrinos perturbations that can reproduce the cold matter linear evolution predicted by Boltzmann codes such as CAMB or CLASS with a 0.1% accuracy or below for all redshift relevant to nonlinear structure formation. We use this description, in the first place, to quantify the systematic errors induced by several approximations often assumed in numerical simulations, including the typical set-up of the initial conditions for massive neutrino cosmologies adopted in previous works. We then take advantage of the flexibility of this approach to rescale the late-time linear power spectra to the simulation initial redshift, in order to be as consistent as possible with the dynamics of the N-body code and the approximations it assumes. We implement our method in a public code providing the initial displacements and velocities for cold dark matter and neutrino particles that will allow accurate, i.e. one-percent level, numerical simulations for this cosmological scenario.

Initial conditions for cosmological N-body simulations of the scalar sector of theories of Newtonian, Relativistic and Modified Gravity

We present a description for setting initial particle displacements and field values for simulations of arbitrary metric theories of gravity, for perfect and imperfect fluids with arbitrary characteristics. We extend the Zel'dovich Approximation to nontrivial theories of gravity, and show how scale dependence implies curved particle paths, even in the entirely linear regime of perturbations. For a viable choice of Effective Field Theory of Modified Gravity, initial conditions set at high redshifts are affected at the level of up to 5% at Mpc scales, which exemplifies the importance of going beyond Λ-Cold Dark Matter initial conditions for modifications of gravity outside of the quasi-static approximation. In addition, we show initial conditions for a simulation where a scalar modification of gravity is modelled in a Lagrangian particle-like description. Our description paves the way for simulations and mock galaxy catalogs under theories of gravity beyond the standard model, crucial for progress towards precision tests of gravity and cosmology.

Higher-order Lagrangian perturbative theory for the Cosmic Web

AbstractZel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

Scale dependence of halo bispectrum from non-Gaussian initial conditions in cosmological N-body simulations

We study the halo bispectrum from non-Gaussian initial conditions. Based on a set of large N-body simulations starting from initial density fields with local type non-Gaussianity, we find that the halo bispectrum exhibits a strong dependence on the shape and scale of Fourier space triangles near squeezed configurations at large scales. The amplitude of the halo bispectrum roughly scales as fNL2. The resultant scaling on the triangular shape is consistent with that predicted by Jeong & Komatsu based on perturbation theory. We systematically investigate this dependence with varying redshifts and halo mass thresholds. It is shown that the fNL dependence of the halo bispectrum is stronger for more massive haloes at higher redshifts. This feature can be a useful discriminator of inflation scenarios in future deep and wide galaxy redshift surveys.

Initial condition problem for cosmological N-body simulations

For a long time, the Lagrangian linear perturbation (Zel'dovich approximation, ZA) is used for initial conditions for cosmological N-body simulations. Recently, Crocce et al. (2006) proposed the improvement of the initial conditions. They applied Lagrangian second-order perturbation (2LPT) for the initial condition. Then they calculated the Lagrangian linear perturbation and showed that 2LPT initial conditions improve the evolution of non-Gaussianity for the density fluctuation in the Universe. Here we have one question. Although 2LPT initial conditions improve the cosmological N -body simulation, is 2LPT initial conditions sufficient? To answer this question, in addition to the ZA and 2LPT, we also calculate the non-Gaussianity with the initial conditions based on third-order Lagrangian perturbation theory (3LPT). Then we show reasonable order of perturbation and redshift for the initial conditions.

Vlasov limit and discreteness effects in cosmological N-body simulations

We present the problematic of controlling the discreteness effects in cosmological N-body simulations. We describe a perturbative treatment which gives an approximation describing the evolution under self-gravity of a lattice perturbed from its equilibrium, which allows to trace the evolution of the fully discrete distribution until the time when particles approach one another (“shell-crossing”). Perturbed lattices are typical initial conditions for cosmological N-body simulations and thus we can describe precisely the early time evolution of these simulations. A quantitative comparison with fluid Lagrangian theory permits to study discreteness effects in the linear regime of the simulations. We show finally some work in progress about quantifying discreteness effects in the non-perturbative (highly non-linear) regime of cosmological N-body simulations by evolving different discretizations of the same continuous density field.

Initial Conditions to CosmologicalN‐Body Simulations, or, How to Run an Ensemble of Simulations

The conventional method of generating initial conditions for cosmological N-body simulations introduces a significant error in the real-space statistical properties of the particles. More specifically, the finite box size leads to a significant underestimate of σ8, the correlation function, and nonlinear effects. I implement a method of generating initial conditions for N-body simulations that accurately models the real-space statistical properties, such as the mass variance in spheres and the correlation function. The method requires running ensembles of simulations because the power in the DC mode is no longer assumed to be zero. For moderately sized boxes, I demonstrate that the new method corrects the underestimate in the mass variance in spheres and the shape of the correlation function. I also argue that subtracting Poisson noise from the power spectrum is a dangerous practice. Code to generate initial conditions to second order in Lagrangian perturbation theory with the new method is available from the author.

A method of generating initial conditions for cosmological N-body simulations

We investigate the possibility of generating initial conditions for cosmological N-body simulations by simulating a system whose correlations at thermal equilibrium approximate well those of cosmological density perturbations. The system is an appropriately modified version of the standard ``one component plasma'' (OCP). We show first how a well-known semianalytic method can be used to determine the potential required to produce the desired correlations, and then verify our results for some cosmological type spectra with simulations of the full molecular dynamics. The advantage of the method, compared to the standard one, is that it gives by construction an accurate representation of both the real and reciprocal space correlation properties of the theoretical model. Furthermore the distributions are also statistically homogeneous and isotropic. We discuss briefly the modifications needed to implement the method to produce configurations appropriate for large N-body simulations in cosmology, and also the generation of initial velocities in this context.

Peak and gravity constraints in Gaussian primordial density fields: an application of the Hoffman-Ribak method

We develop an algorithm for setting up initial Gaussian random density and velocity fields containing one or more peaks or dips, in an arbitrary cosmological scenario. The intention is to generate appropriate initial conditions for cosmological N-body simulations that focus on the evolution of the progenitors of the present-day galaxies and clusters. The procedure is an application of the direct and accurate prescription of Hoffman & Ribak (1991) for generating constrained random fields. For each peak a total of 21 physical characteristics can be specified, including its scale, position, density Hessian, velocity, and velocity gradient. The velocity (or, equivalently, gravity) field constrants are based on a generalization of the formalism developed by Bardeen et al. (1986). The resulting density field is sculpted such that it induces the desired amount of net gravitational and tidal forces. We provide a detailed mathematical presentation of the formalism. Afterwards we provide analytical estimates of the likelihood of the imposed constraints. Amongst others, it is shown that the tidal field has a strong tendency to align itself along the principal axes of the mass tensor. The method is illustrated by means of some concrete examples. In addition to the illustration of constraint-field correlation functions and how they add up to the mean fields, followed by illustrations of the variance characteristics of field realizations, we concentrate in particular on the consequences of imposing gravitational field constraints (or, equivalent in the linear regime for growing mode fluctuations, peculiar velocity field constraints).

Non-Gaussian initial conditions in cosmological N-body simulations – III. Groups in Cold Dark Matter models

Group catalogues are obtained in N-body simulations of the large-scale structure of the Universe with non-Gaussian initial conditions in a Cold Dark Matter cosmogony. Groups of particles are defined by the standard percolation algorithm with linking parameter b = 0.25 in units of the mean interparticle distance. Grouping properties are found to strongly depend on the statistics of the underlying mass distributions. By applying different tests, the clustering and the topology of the group distribution, the environmental properties of the groups and their internal geometric and dynamical features are analysed

Non-Gaussian initial conditions in cosmological N-body simulations - II. Cold Dark Matter models

Results are reported on N-body simulations of the large-scale structure of the Universe starting from non-Gaussian initial conditions in a cold dark matter cosmogony. Three multiplicative models are condidered where the peculiar gravitational potential is obtained by performing a non-linear transformation on a Gaussian random field: while keeping the standard form for the initial power spectrum, this procedure provides highly non-random phases. The resulting distributions in space and velocity are analysed by different statistical tests and compared with the evolution of a standard Gaussian model with the same initial amplitude.

Non-Gaussian initial conditions in cosmological N-body simulations — I. Space-uncorrelated models

Summary Results are reported on N-body simulations of the large-scale structure of the Universe starting from non-Gaussian, space-uncorrelated, initial conditions: specifically, we consider two hierarchical models and the lognormal statistics for the initial probability distribution. These models share two common properties: they fulfil the positive mass constraint (δM ≥ − 1) and they have positive skewness (〈δM3〉>0). The resulting distributions, both in space and velocity, are analysed by means of many statistical tests, and compared with an evolved reference Poisson model. The different starting conditions keep their effects after many expansion times as shown in particular by the cluster analysis and by the quadrupole statistics: the evolved nonGaussian distributions show the existence of elongated and/or flattened configurations in excess of the evolved Poisson model. The velocity field, analysed in terms of the cosmic Mach number, does not reveal relevant changes with respect to the initially Gaussian model. In general we find that the different models are better discriminated by their geometry (like the percolation curve and the amount of filamentariness) than by their clustering properties.