Euclid preparation: IX. EuclidEmulator2-power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent level accurate emulation is now supported in the eight-dimensional parameter space of w(0)w(a)CDM+Sigma m(nu) models between redshift z = 0 and z = 3 for spatial scales within the range . In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy, and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 3000(3) particles in boxes of 1(h(-1)Gpc)(3) volumes based on paired-and-fixed initial conditions, and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter w(a) significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors such as HALOFIT, HMCode, and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of or better for and z

The DESI N-body Simulation Project - II. Suppressing sample variance with fast simulations

Andrei Variu, Yu Yu, Hanyu Zhang, Cheng Zhao

Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise three-dimensional map of our Universe. The survey effective volume reaches similar to 20 h(-3) Gpc(3). It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. ABACUSSUMMIT is a suite of high-resolution dark-matter-only simulations designed for this purpose, with 200 h(-3) Gpc(3) (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide a more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi-N-body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variance than the expected DESI statistical variance at the scales we are interested in, e.g. k < 0.3 h Mpc(-1) for the halo power spectrum. In addition, it can significantly suppress the sample variance of the halo bispectrum. We further generalize the method for other cosmologies with only one realization in ABACUSSUMMIT suite to extend the effective volume similar to 20 times. In summary, our proposed strategy of combining high-fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data.

OXFORD UNIV PRESS2022

One simulation to have them all: performance of the Bias Assignment Method against N-body simulations

Cheng Zhao

In this paper, we demonstrate that the information encoded in one single (sufficiently large) N-body simulation can be used to reproduce arbitrary numbers of halo catalogues, using approximated realizations of dark matter density fields with different initial conditions. To this end, we use as a reference one realization (from an ensemble of 300) of the Minerva N-body simulations and the recently published Bias Assignment Method to extract the local and non-local bias linking the halo to the dark matter distribution. We use an approximate (and fast) gravity solver to generate 300 dark matter density fields from the down-sampled initial conditions of the reference simulation and sample each of these fields using the halo-bias and a kernel, both calibrated from the arbitrarily chosen realization of the reference simulation. We show that the power spectrum, its variance, and the three-point statistics are reproduced within similar to 2 per cent (up to k similar to 1.0 h Mpc(-1)), similar to 5 - 10 per cent, and similar to 10 per cent, respectively. Using a model for the real space power spectrum (with three free bias parameters), we show that the covariance matrices obtained from our procedure lead to parameter uncertainties that are compatible within similar to 10 per cent with respect to those derived from the reference covariance matrix, and motivate approaches that can help to reduce these differences to similar to 1 per cent. Our method has the potential to learn from one simulation with moderate volumes and high-mass resolution and extrapolate the information of the bias and the kernel to larger volumes, making it ideal for the construction of mock catalogues for present and forthcoming observational campaigns such as Euclid or DESI.

OXFORD UNIV PRESS2020

A Framework for Numerical Simulations of Structure Formation

Claude Becker

In the absence of a full analytical treatment of nonlinear structure formation in the universe, numerical simulations provide the critical link between the properties of the underlying model and the features of the observed structures. Currently N-body simulations are the main tool to study structure growth. We explore an alternative framework for numerical simulations of structure formation. The underlying idea is to replace the long-range gravitational force in the Vlasov-Poisson system by a purely local interaction. To this end we trade the classical phase space distribution for its quantum mechanical counterpart, the Wigner distribution function. Its dynamical equation is equivalent to the Schrödinger equation and reduces to the Vlasov equation in the formal semi-classical limit. The proposed framework allows in principle to simulate systems with arbitrary phase space distributions and could for instance be beneficial for simulations of warm dark matter, where the velocity dispersion is important. We discuss several methods to obtain a set of wavefunctions whose Wigner distribution is close to a given initial phase space distribution function. An auxiliary gauge field is introduced to mediate the gravitational interaction, thereby obtaining a local Schrödinger-Maxwell system. We also use the ideas of lattice gauge theories to obtain a fully gauge-invariant discretization of the equations of motion. Their iterative solution was implemented in a three-dimensional simulation code. We discuss its computational complexity and memory requirements. Several testbed simulations were performed with this method. We compared the gravitational collapse of a Gaussian wavefunction with an independent numerical solution of the spherically symmetric Schrödinger-Newton system. The results were found to be in good agreement. Finally, a simple example of the growth of cosmic perturbations is investigated within our framework. We conclude by outlining various possible directions to optimize and develop our method.

EPFL2011

A Framework for Numerical Simulations of Structure Formation

Claude Becker

EPFL2011