We present sCOLA -- an extension of the N-body COmoving Lagrangian Acceleration (COLA) method to the spatial domain. Similar to the original temporal-domain COLA, sCOLA is an N-body method for solving for large-scale structure in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory. Incorporating the sCOLA method in an N-body code allows one to gain computational speed by capturing the gravitational potential from the far field using perturbative techniques, while letting the N-body code solve only for the near field. The far and near fields are completely decoupled, effectively localizing gravity for the N-body side of the code. Thus, running an N-body code for a small simulation volume using sCOLA can reproduce the results of a standard N-body run for the same small volume embedded inside a much larger simulation. We demonstrate that sCOLA can be safely combined with the original temporal-domain COLA. sCOLA can be used as a method for performing zoom-in simulations. It also allows N-body codes to be made embarrassingly parallel, thus allowing for efficiently tiling a volume of interest using grid computing. Moreover, sCOLA can be useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering. Surveys that will benefit the most are ones with large aspect ratios, such as pencil-beam surveys, where sCOLA can easily capture the effects of large-scale transverse modes without the need to substantially increase the simulated volume. As an illustration of the method, we present proof-of-concept zoom-in simulations using a freely available sCOLA-based N-body code.
We introduce $\texttt{Hi-COLA}$, a code designed to run fast, approximate $\textit{N}$-body simulations of non-linear structure formation in reduced Horndeski gravity. Given an input Lagrangian, $\texttt{Hi-COLA}$ dynamically constructs the appropriate field equations and consistently solves for the cosmological background, linear growth, and screened fifth force of that theory. Hence $\texttt{Hi-COLA}$ is a general, adaptable, and useful tool that allows the mildly non-linear regime of many Horndeski theories to be investigated for the first time, at low computational cost. In this work, we f…
We investigate the viability of producing galaxy mock catalogues with COmoving Lagrangian Acceleration (COLA) simulations in Modified Gravity (MG) models employing the Halo Occupation Distribution (HOD) formalism. In this work, we focus on two theories of MG: $f(R)$ gravity with the chameleon mechanism, and a braneworld model (nDGP) that incorporates the Vainshtein mechanism. We use a suite of full $N$-body simulations in MG as a benchmark to test the accuracy of COLA simulations. At the level of Dark Matter (DM), we show that COLA accurately reproduces the matter power spectrum up to $k \sim …
Modeling nonlinear scales for dynamical dark energy cosmologies with COLA
CBPF - Brazilian Center for Research in Physics（巴西物理研究中心）；Instituto de Física Teórica da Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）；Department of Physics & Astronomy, Stony Brook University（石溪大学物理与天文学系）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学陈省身理论物理研究所）
We compare and validate COLA (COmoving Lagrangian Acceleration) simulations against existing emulators in the literature, namely Bacco and Euclid Emulator 2. Our analysis focuses on the non-linear response function, i.e., the ratio between the non-linear dark matter power spectrum in a given cosmology with respect to a pre-defined reference cosmology, which is chosen to be the Euclid Emulator 2 reference cosmology in this paper. We vary three cosmological parameters, the total matter density, the amplitude of the primordial scalar perturbations and the spectral index. By comparing the COLA non…
One of the main objectives of stage IV galaxy surveys is to constrain gravity on cosmological scales. To this end, it is crucial to make accurate theoretical predictions in the nonlinear regime of structure formation in order to maximise the scientific return. This is possible at a relatively low computational cost thanks to COLA simulations, an approximate and much faster alternative to full $N$-body simulations. In this thesis, we focus on two modified gravity theories, $f(R)$ and nDGP, and present an analysis of how COLA simulations can be combined with empirical models for the galaxy-halo …
We train convolutional neural networks to correct the output of fast and approximate N-body simulations at the field level. Our model, Neural Enhanced COLA --NECOLA--, takes as input a snapshot generated by the computationally efficient COLA code and corrects the positions of the cold dark matter particles to match the results of full N-body Quijote simulations. We quantify the accuracy of the network using several summary statistics, and find that NECOLA can reproduce the results of the full N-body simulations with sub-percent accuracy down to $k\simeq1~h{\rm Mpc}^{-1}$. Furthermore, the mode…
The tomographic AP method is so far the best method in separating the Alcock-Paczynski (AP) signal from the redshift space distortion (RSD) effects and deriving powerful constraints on cosmological parameters using the $\lesssim40h^{-1}\ \rm Mpc$ clustering region. To guarantee that the method can be easily applied to the future large scale structure (LSS) surveys, we study the possibility of estimating the systematics of the method using fast simulation method. The major contribution of the systematics comes from the non-zero redshift evolution of the RSD effects, which is quantified by $\hat…
Field Level Neural Network Emulator for Cosmological N-body Simulations
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Stony Brook University（石溪大学）；Flatiron Institute（熨斗研究所）；Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；Princeton University（普林斯顿大学）；Simons Foundation（西蒙斯基金会）
Fast N-body PM simulations with a small number of time steps such as FastPM or COLA have been remarkably successful in modeling the galaxy statistics, but their lack of small scale force resolution and long time steps cannot give accurate halo matter profiles or matter power spectrum. High resolution N-body simulations can improve on this, but lack baryonic effects, which can only be properly included in hydro simulations. Here we present a scheme to calibrate the fast simulations to mimic the precision of the hydrodynamic simulations or high resolution N-body simulations. The scheme is based …
We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constrains related to growth rate of structure, Alcock-Paczynski distortions and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE-COLA, Pinocchio and PeakPatch), methods that rely on halo assignment schemes onto dark-matter overdensities calibrated with a target N…
