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Title: Speeding up N -body simulations of modified gravity: chameleon screening models

Abstract

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running verymore » high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.« less

Authors:
; ; ;  [1];  [2]; ;  [3];  [4]
  1. Institute for Computational Cosmology, Department of Physics, Durham University, Durham DH1 3LE (United Kingdom)
  2. Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)
  3. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom)
  4. National Astronomy Observatories, Chinese Academy of Science, Beijing, 100012 (China)
Publication Date:
OSTI Identifier:
22680005
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; COMPUTERIZED SIMULATION; CONVERGENCE; EFFICIENCY; GRAVITATION; INSTABILITY; ITERATIVE METHODS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; PERFORMANCE; RESOLUTION; STANDARD MODEL; VELOCITY

Citation Formats

Bose, Sownak, Li, Baojiu, He, Jian-hua, Llinares, Claudio, Barreira, Alexandre, Hellwing, Wojciech A., Koyama, Kazuya, and Zhao, Gong-Bo, E-mail: sownak.bose@durham.ac.uk, E-mail: baojiu.li@durham.ac.uk, E-mail: barreira@mpa-garching.mpg.de, E-mail: jianhua.he@durham.ac.uk, E-mail: wojciech.hellwing@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: claudio.llinares@durham.ac.uk, E-mail: gbzhao@nao.cas.cn. Speeding up N -body simulations of modified gravity: chameleon screening models. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/02/050.
Bose, Sownak, Li, Baojiu, He, Jian-hua, Llinares, Claudio, Barreira, Alexandre, Hellwing, Wojciech A., Koyama, Kazuya, & Zhao, Gong-Bo, E-mail: sownak.bose@durham.ac.uk, E-mail: baojiu.li@durham.ac.uk, E-mail: barreira@mpa-garching.mpg.de, E-mail: jianhua.he@durham.ac.uk, E-mail: wojciech.hellwing@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: claudio.llinares@durham.ac.uk, E-mail: gbzhao@nao.cas.cn. Speeding up N -body simulations of modified gravity: chameleon screening models. United States. doi:10.1088/1475-7516/2017/02/050.
Bose, Sownak, Li, Baojiu, He, Jian-hua, Llinares, Claudio, Barreira, Alexandre, Hellwing, Wojciech A., Koyama, Kazuya, and Zhao, Gong-Bo, E-mail: sownak.bose@durham.ac.uk, E-mail: baojiu.li@durham.ac.uk, E-mail: barreira@mpa-garching.mpg.de, E-mail: jianhua.he@durham.ac.uk, E-mail: wojciech.hellwing@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: claudio.llinares@durham.ac.uk, E-mail: gbzhao@nao.cas.cn. Wed . "Speeding up N -body simulations of modified gravity: chameleon screening models". United States. doi:10.1088/1475-7516/2017/02/050.
@article{osti_22680005,
title = {Speeding up N -body simulations of modified gravity: chameleon screening models},
author = {Bose, Sownak and Li, Baojiu and He, Jian-hua and Llinares, Claudio and Barreira, Alexandre and Hellwing, Wojciech A. and Koyama, Kazuya and Zhao, Gong-Bo, E-mail: sownak.bose@durham.ac.uk, E-mail: baojiu.li@durham.ac.uk, E-mail: barreira@mpa-garching.mpg.de, E-mail: jianhua.he@durham.ac.uk, E-mail: wojciech.hellwing@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: claudio.llinares@durham.ac.uk, E-mail: gbzhao@nao.cas.cn},
abstractNote = {We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.},
doi = {10.1088/1475-7516/2017/02/050},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 02,
volume = 2017,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}
  • We introduce and demonstrate the power of a method to speed up current iterative techniques for N-body modified gravity simulations. Our method is based on the observation that the accuracy of the final result is not compromised if the calculation of the fifth force becomes less accurate, but substantially faster, in high-density regions where it is relatively weak due to screening. We focus on the nDGP model which employs Vainshtein screening, and test our method by running AMR simulations in which the fifth force on the finer levels of the mesh (high density) is not obtained iteratively, but instead interpolatedmore » from coarser levels. The calculation of the standard gravity component of the force still employs the full AMR structure. We show that the impact this has on the matter power spectrum is below 1% for k < 5h/Mpc at 0z = , and even smaller at higher redshift. The impact on halo properties is also small (∼< 3% for abundance, profiles, mass; and ∼< 0.05% for positions and velocities). The method can boost the performance of modified gravity simulations by more than a factor of 10. This allows them to run on timescales similar to GR simulations and to push them to resolution levels that were previously hard to achieve.« less
  • In this work we systematically study the linear and nonlinear structure formation in chameleon theories of modified gravity, using a generic parameterisation which describes a large class of models using only 4 parameters. For this we have modified the N-body simulation code ecosmog to perform a total of 65 simulations for different models and parameter values, including the default ΛCDM. These simulations enable us to explore a significant portion of the parameter space. We have studied the effects of modified gravity on the matter power spectrum and mass function, and found a rich and interesting phenomenology where the difference withmore » the ΛCDM paradigm cannot be reproduced by a linear analysis even on scales as large as k ∼ 0.05 hMpc{sup −1}, since the latter incorrectly assumes that the modification of gravity depends only on the background matter density. Our results show that the chameleon screening mechanism is significantly more efficient than other mechanisms such as the dilaton and symmetron, especially in high-density regions and at early times, and can serve as a guidance to determine the parts of the chameleon parameter space which are cosmologically interesting and thus merit further studies in the future.« less
  • To respect the nature of discrete parts in a system, stochastic simulation algorithms (SSAs) must update for each action (i) all part counts and (ii) each action's probability of occurring next and its timing. This makes it expensive to simulate biological networks with well-connected “hubs” such as ATP that affect many actions. Temperature and volume also affect many actions and may be changed significantly in small steps by the network itself during fever and cell growth, respectively. Such trends matter for evolutionary questions, as cell volume determines doubling times and fever may affect survival, both key traits for biological evolution.more » Yet simulations often ignore such trends and assume constant environments to avoid many costly probability updates. Such computational convenience precludes analyses of important aspects of evolution. Here we present “Lazy Updating,” an add-on for SSAs designed to reduce the cost of simulating hubs. When a hub changes, Lazy Updating postpones all probability updates for reactions depending on this hub, until a threshold is crossed. Speedup is substantial if most computing time is spent on such updates. We implemented Lazy Updating for the Sorting Direct Method and it is easily integrated into other SSAs such as Gillespie's Direct Method or the Next Reaction Method. Testing on several toy models and a cellular metabolism model showed >10× faster simulations for its use-cases—with a small loss of accuracy. Thus we see Lazy Updating as a valuable tool for some special but important simulation problems that are difficult to address efficiently otherwise.« less
  • 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 gravitymore » 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.« less
  • Theories in which gravity is weaker on cosmological scales have been proposed to explain the observed acceleration of the universe. The nonlinear regime in such theories is not well studied, though it is likely that observational tests of structure formation will lie in this regime. A class of alternative gravity theories may be approximated by modifying Poisson's equation. We have run N-body simulations of a set of such models to study the nonlinear clustering of matter on 1-100 Mpc scales. We find that nonlinear gravity enhances the deviations of the power spectrum of these models from standard gravity. This occursmore » due to mode coupling, so that models with an excess or deficit of large-scale power (at k<0.2 Mpc{sup -1}) lead to deviations in the power spectrum at smaller scales as well (up to k{approx}1 Mpc{sup -1}), even though the linear spectra match very closely on the smaller scales. This makes it easier to distinguish such models from general relativity using the three-dimensional power spectrum probed by galaxy surveys and the weak lensing power spectrum. If the potential for light deflection is modified in the same way as the potential that affects the dark matter, then weak lensing constrains deviations from gravity even more strongly. Our simulations show that, even with a modified potential, gravitational evolution is approximately universal. Based on this, the Peacock-Dodds approach can be adapted to get an analytical fit for the nonlinear power spectra of alternative gravity models, though the recent Smith et al. formula is less successful. Our conclusions extend to models with modifications of gravity on scales of 1-20 Mpc. We also use a way of measuring projected power spectra from simulations that lowers the sample variance, so that fewer realizations are needed to reach a desired level of accuracy.« less