How is the value of the field on the physical boundary of a refinement determined?

The value of the field on this physical boundary is computed at the beginning of the relaxation process and kept unchanged after that until a converged solution in the active cells are obtained.

What is the simplest test of the f(R) equation solver?

as the simplest test of the f(R) equation solver, one has to show that in such a homogeneous field, given some random guess of f̃R on the cells of the simulation mesh, after a reasonable number of GaussSeidel relaxation sweeps, the solution converges to the above background value.

How did the authors measure the spectra of the f(R) gravity model?

As one cosmological test, the authors have performed simulations for the f(R) gravity model with |fR0| = 10−5 using a 100h−1Mpc simulation box and measured their matter power spectra.

How can one correct the fine-level solution to H?

Once an approximate coarser-level solution to δφH is obtained, say δ̂φ H , one can correct the fine-level solution usingφ̂h ← φ̂h +

What is the case where the regular domain grid is refined only once?

Consider the case where the regular domain grid is refined only once, in regions where the density value exceeds some certain threshold (we shall call this a two-level problem, and in the present numeric example the coarse and fine levels are respectively levels 8 and 9).

How do the authors find the small scale structure in the f(R) gravity?

the authors find the small-scale structure in the f(R) gravity to be quite sensitive to the convergence criterion of the f(R) equation solver as well as the size of the simulation box, the refinement criterion etc., and a thorough study needs to be conducted to clarify these issues before systematic simulations of the f(R) gravity are performed.

Open AccessJournal Article10.1088/1475-7516/2012/01/051

ECOSMOG: An Efficient Code for Simulating Modified Gravity

Baojiu Li, +4 more

- 06 Oct 2011

- arXiv: Cosmology and Nongalactic Astroph...

199

TL;DR: A new code, ECOSMOG, to run N-body simulations for a wide class of modified gravity and dynamical dark energy theories, based on the RAMSES code, which solves the Poisson equation on adaptively refined meshes to gain high resolutions in the high-density regions.

Abstract: We introduce a new code, ECOSMOG, to run N-body simulations for a wide class of modified gravity and dynamical dark energy theories. These theories generally have one or more new dynamical degrees of freedom, the dynamics of which are governed by their (usually rather nonlinear) equations of motion. Solving these non-linear equations has been a great challenge in cosmology. Our code is based on the RAMSES code, which solves the Poisson equation on adaptively refined meshes to gain high resolutions in the high-density regions. We have added a solver for the extra degree(s) of freedom and performed numerous tests for the f(R) gravity model as an example to show its reliability. We find that much higher efficiency could be achieved compared with other existing mesh/grid-based codes thanks to two new features of the present code: (1) the efficient parallelisation and (2) the usage of the multigrid relaxation to solve the extra equation(s) on both the regular domain grid and refinements, giving much faster convergence even under much more stringent convergence criteria. This code is designed for performing high-accuracy, high-resolution and large-volume cosmological simulations for modified gravity and general dark energy theories, which can be utilised to test gravity and the dark energy hypothesis using the upcoming and future deep and high-resolution galaxy surveys.

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2. Why does the TSC scheme have a more smoother density field?

Because in the TSC density assignment scheme a particle’s cloud 3 spreads more than in the CIC scheme, the resulted density field will be smoother and as a result the authors expect less small-scale structure from N -body simulations.

3. Why is the density field less developed?

This is because the clustering is less developed and the cell size is larger, so that smaller scales are not resolved as well as for smaller box sizes.

4. How many CPUs can run a simulation with a 500hp box?

With 80 CPUs, their simulations with 500h−1Mpc box size can finish within a couple of hours, in contrast to about 24 hours for the simulations with 100h−1Mpc box size.

FIG. 4. (Colour online) Solutions of fR in a one-dimensional (x-direction) Gaussian-type density configuration constructed using Eq. (43), for the models with |fR0| = 10 −5 and α = 0.5 (red circles), 0.99 (green triangles) and 0.999 (blue squares). The solid curves are the corresponding analytical results from Eq. (45). A simulation box with side length of 256h−1Mpc and 256 grid cells on each side is used in the computation and the f(R) equation is only solved on the regular domain grid. x is in physical units.

FIG. 3. (Colour online) Solutions of fR in a one-dimensional (x-direction) sine density field constructed using Eq. (41), for three models with |fR0| = 10 −6 (blue triangles), 10−5 (green filled circles) and 10−4 (red squares) respectively. The solid curves are the corresponding analytical results. A simulation box with side length of 256h−1Mpc and 256 grid cells on each side is used in the computation. x is in physical units.

FIG. 10. (Colour online) The wallclock time of the f(R) equation solver as a function of the number of CPUs used in the parallelised computation. The actual measurement is shown as the black solid curve, while the blue dashed line is a linear scaling just for comparison. It is obvious that the time-CPU number scaling is approximately linear for CPU numbers up to ∼ 100.

FIG. 9. (Colour online) The reduction of the residual for the f(R) equation for three models: |fR0| = 10 −4 with a sine-type density field as discussed above (red squares), |fR0| = 10 −6 with a sine-type density field (green circles) and |fR0| = 10 −4 for a point mass discussed above (blue triangles). The results using a single grid are represented by symbols connected by solid curves, while those using the multigrid method (arranged by V-cycles) by symbols connected by dashed curves.

TABLE I. A brief summary of the key features of the three known grid-based codes for N-body simulations in modified gravity and/or dynamical dark energy theories. Here OC stands for Oyaizu Code, and by MLAPM we mean the modified version to include the multigrid solver for the extra degree(s) of freedom.

FIG. 8. (Colour online) Upper Panel: Comparison of the nonlinear matter power spectra using the TSC (blue diamonds) and CIC (red squares) density assignment schemes to that obtained using Smith et al. fit (black solid curve). Lower Panel: The relative differences of the TSC and CIC power spectra with respect to that of the Smith et al. fit. The dashed black line is zero identically. The cosmological simulations here use a cubic box with size 100h−1Mpc and 256 cells on each side of the domain grid. The error bars show the sample variance over 5 different realisations. All results are at redshift 0.

Citations

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Computer simulation using particles

R W Hockney, +1 more

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TL;DR: In this article, the authors review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence and tachyon.

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R W Hockney, +1 more

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TL;DR: Computer experiments using particle models A one-dimensional plasma model The simulation program Time integration schemes The particle-mesh force calculation The solution of field equations Collisionless particle models Particle-particles/particle/particles algorithms Plasma simulation Semiconductor device simulation Astrophysics

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f ( R ) theories of gravity

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TL;DR: In this article, the authors present a review of the most important aspects of the different classes of modified gravity theories, including higher-order curvature invariants and metric affine.

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The Confrontation Between General Relativity and Experiment

Clifford M. Will

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ECOSMOG: An Efficient Code for Simulating Modified Gravity

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AI Agents for this Paper

Most frequently asked questions

1. What are the contributions in "Ecosmog: an efficient code for simulating modified gravity" ?

2. Why does the TSC scheme have a more smoother density field?

3. Why is the density field less developed?

4. How many CPUs can run a simulation with a 500hp box?

5. How is the value of the field on the physical boundary of a refinement determined?

6. What is the simplest test of the f(R) equation solver?

7. How did the authors measure the spectra of the f(R) gravity model?

8. How can one correct the fine-level solution to H?

9. What is the case where the regular domain grid is refined only once?

10. How do the authors find the small scale structure in the f(R) gravity?

Figures

Citations

Testing general relativity with present and future astrophysical observations

Cosmology and Fundamental Physics with the Euclid Satellite

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

Cosmological Tests of Modified Gravity

Cosmology with cosmic shear observations: a review

References

Computer simulation using particles

Dynamics of dark energy

Computer Simulation Using Particles

f ( R ) theories of gravity

The Confrontation Between General Relativity and Experiment

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