# 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 »

- Authors:

- Institute for Computational Cosmology, Department of Physics, Durham University, Durham DH1 3LE (United Kingdom)
- Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)
- Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom)
- 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}

}