Simulations of Structure Formation in the Universe

Bertschinger, Edmund

doi:10.1146/annurev.astro.36.1.599

Cited by 277 publications

(281 citation statements)

References 470 publications

(496 reference statements)

Supporting

Mentioning

277

Contrasting

Unclassified

Order By: Relevance

“…[2,3,4]). A fundamental question about such simulations concerns the degree to which they reproduce the evolution of the simulated models.…”

Section: Introductionmentioning

confidence: 99%

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Joyce¹,

Marcos²

2007

Phys. Rev. D

View full text Add to dashboard Cite

The relation between the results of cosmological N-body simulations, and the continuum theoretical models they simulate, is currently not understood in a way which allows a quantification of N dependent effects. In this first of a series of papers on this issue, we consider the quantification of such effects in the initial conditions of such simulations. A general formalism developed in [1] allows us to write down an exact expression for the power spectrum of the point distributions generated by the standard algorithm for generating such initial conditions. Expanded perturbatively in the amplitude of the input (i.e. theoretical, continuum) power spectrum, we obtain at linear order the input power spectrum, plus two terms which arise from discreteness and contribute at large wavenumbers. For cosmological type power spectra, one obtains as expected, the input spectrum for wavenumbers k smaller than that characteristic of the discreteness. The comparison of real space correlation properties is more subtle because the discreteness corrections are not as strongly localised in real space. For cosmological type spectra the theoretical mass variance in spheres and two point correlation function are well approximated above a finite distance. For typical initial amplitudes this distance is a few times the inter-particle distance, but it diverges as this amplitude (or, equivalently, the initial red-shift of the cosmological simulation) goes to zero, at fixed particle density. We discuss briefly the physical significance of these discreteness terms in the initial conditions, in particular with respect to the definition of the continuum limit of N-body simulations.

show abstract

“…[2,3,4]). A fundamental question about such simulations concerns the degree to which they reproduce the evolution of the simulated models.…”

Section: Introductionmentioning

confidence: 99%

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Joyce¹,

Marcos²

2007

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…0.2n Subject heading: methods: n-body simulations 1. INTRODUCTION Numerical simulations of the softened gravitational n-body problem are used to gain insight into the formation, evolution, and structure of gravitational systems ranging from galaxies and clusters of galaxies to the large-scale structure of the universe (Clarke & West 1997;Bertschinger 1998). Since such simulations have been used to invalidate theories (Bertschinger 1998), establishing their trustworthiness is critical.…”

mentioning

confidence: 99%

Shadowing-based Reliability Decay in Softened n -Body Simulations

Hayes

2003

ApJ

View full text Add to dashboard Cite

A shadow of a numerical solution to a chaotic system is an exact solution to the equations of motion that remains close to the numerical solution for a long time. In a collisionless n-body system, we know that particle motion is governed by the global potential rather than by interparticle interactions. As a result, the trajectory of each individual particle in the system is independently shadowable. It is thus meaningful to measure the number of particles that have shadowable trajectories as a function of time. We find that the number of shadowable particles decays exponentially with time as and that for (in units of the local mean interparticleϪmt e e [∼ 0.2, 1] separation ), there is an explicit relationship among the decay constant m, the time step h of the leapfroḡ n integrator, the softening e, and the number of particles N in the simulation. Thus, given N and e, it is possible to precompute the time step h necessary to achieve a desired fraction of shadowable particles after a given length of simulation time. We demonstrate that a large fraction of particles remain shadowable over ∼100 crossing times even if particles travel up to about of the softening length per time step. However, a sharp decrease in the 1 3 number of shadowable particles occurs if the time step increases to allow particles to travel farther than the 1 3 softening length in 1 time step or if the softening is decreased below ∼ . 0.2n

show abstract

“…Here we present a brief review of the N-body simulation code GADGET-2. For more information on the code see Springel (2005) and for a comprehensive review of N-body simulations see Bertschinger (1998 The core of any N-body simulation is the gravity solver. In the PM (particle -mesh) algorithm the density field is realised on a grid and the gravitational potential is constructed by solving Poisson's equation.…”

Section: The Simulation Codementioning

confidence: 99%

Simulations of Dark Energy Cosmologies

Jennings

2012

Springer Theses

View full text Add to dashboard Cite

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source• a link is made to the metadata record in Durham E-Theses• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. No part of this thesis has been submitted elsewhere for any other degree or qualification.The work of others has been duly acknowledged.The copyright of this thesis rests with the author. No quotations from it should be published without the author's prior written consent and information derived from it should be acknowledged. AbstractFuture galaxy redshift surveys will make high precision measurements of the cosmic expansion history and the growth of structure which will potentially allow us to distinguish between different scenarios for the accelerating expansion of the Universe. In this thesis we study the nonlinear growth of cosmic structure in different dark energy models, using ultra-large volume N-body simulations. We measure key observables such as the growth of large scale structure, the halo mass function and baryonic acoustic oscillations.We study the power spectrum in redshift space in ΛCDM and quintessence dark energy models and test predictions for the form of the redshift space distortions. An improved model for the redshift space power spectrum, including the non-linear velocity divergence power spectrum, is presented. We have found a density-velocity relation which is cosmology independent and which relates the non-linear velocity divergence spectrum to the non-linear matter power spectrum. We provide a formula which generates the non-linear velocity divergence P(k) at any redshift, using only the non-linear matter power spectrum and the linear growth factor at the desired redshift. We also demonstrate for the first time that competing cosmological models with identical expansion histories -one with a scalar field and the other with a time-dependent change to Newton's gravitational constant -can indeed be distinguished by a measurement of the rate at which structures grow.Our calculations show that linear theory models for the power spectrum in redshift space fail to recover the correct growth rate on surprisingly large scales, leading to catastrophic systematic errors. Improved theoretical models, which have been calibrated against simulations, are needed to exploit the exquisitely accurate clustering measurements expected from future surveys.

show abstract

Simulations of Structure Formation in the Universe

Cited by 277 publications

References 470 publications

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Shadowing-based Reliability Decay in Softened n -Body Simulations

Simulations of Dark Energy Cosmologies

Contact Info

Product

Resources

About