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Register a new userNon-linear evolution of f(R) cosmologies II: power spectrum
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We carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances the force of gravity below the inverse mass or Compton scale of the scalar. The simulations exhibit the so-called chameleon mechanism, necessary for satisfying local constraints on gravity, where this scale depends on environment, in particular the depth of the local gravitational potential. We find that the chameleon mechanism can substantially suppress the enhancement of power spectrum in the non-linear regime if the background field value is comparable to or smaller than the depth of the gravitational potentials of typical structures. Nonetheless power spectrum enhancements at intermediate scales remain at a measurable level for models even when the expansion history is indistinguishable from a cosmological constant, cold dark matter model. Simple scaling relations that take the linear power spectrum into a non-linear spectrum fail to capture the modifications of f(R) due to the change in collapsed structures, the chameleon mechanism, and the time evolution of the modifications.
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We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f(R) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a non-linear Poisson equation for the scalar degree of freedom introduced by the f(R) modifications. We detail the method to efficiently solve the non-linear Poisson equation by using a Newton-Gauss-Seidel relaxation scheme coupled with multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f(R) physics. In general, we find that the f(R) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ~20% for large but observationally allowed f(R) modifications. More detailed study of the non-linear f(R) effects on the power spectrum are presented in a companion paper.
The statistical properties of dark matter halos, the building blocks of cosmological observables associated with structure in the universe, offer many opportunities to test models for cosmic acceleration, especially those that seek to modify gravitational forces. We study the abundance, bias and profiles of halos in cosmological simulations for one such model: the modified action f(R) theory. In the large field regime that is accessible to current observations, enhanced gravitational forces raise the abundance of rare massive halos and decrease their bias but leave their (lensing) mass profiles largely unchanged. This regime is well described by scaling relations based on a modification of spherical collapse calculations. In the small field regime, enhanced forces are suppressed inside halos and the effects on halo properties are substantially reduced for the most massive halos. Nonetheless, the scaling relations still retain limited applicability for the purpose of establishing conservative upper limits on the modification to gravity.
Testing a subset of viable cosmological models beyond General Relativity (GR), with implications for cosmic acceleration and the Dark Energy associated with it, is within the reach of Rubin Observatory Legacy Survey of Space and Time (LSST) and a part of its endeavor. Deviations from GR-w(z)CDM models can manifest in the growth rate of structure and lensing, as well as in screening effects on non-linear scales. We explore the constraining power of small-scale deviations predicted by the f(R) Hu-Sawicki Modified Gravity (MG) candidate, by emulating this model with COLA (COmoving Lagrangian Acceleration) simulations. We present the experimental design, data generation, and interpolation schemes in cosmological parameters and across redshifts for the emulation of the boost in the power spectra due to Modified Gravity effects. Three preliminary applications of the emulator highlight the sensitivity to cosmological parameters, Fisher forecasting and Markov Chain Monte Carlo inference for a fiducial cosmology. This emulator will play an important role for future cosmological analysis handling the formidable amount of data expected from Rubin Observatory LSST.
We investigate the qualitative evolution of (D+1)-dimensional cosmological models in f(R) gravity for the general case of the function f(R). The analysis is specified for various examples, including the (D+1)-dimensional generalization of the Starobinsky model, models with polynomial and exponential functions. The cosmological dynamics are compared in the Einstein and Jordan representations of the corresponding scalar-tensor theory. The features of the cosmological evolution are discussed for Einstein frame potentials taking negative values in certain regions of the field space.
We introduce an emulator approach to predict the non-linear matter power spectrum for broad classes of beyond-$Lambda$CDM cosmologies, using only a suite of $Lambda$CDM $N$-body simulations. By including a range of suitably modified initial conditions in the simulations, and rescaling the resulting emulator predictions with analytical `halo model reactions, accurate non-linear matter power spectra for general extensions to the standard $Lambda$CDM model can be calculated. We optimise the emulator design by substituting the simulation suite with non-linear predictions from the standard {sc halofit} tool. We review the performance of the emulator for artificially generated departures from the standard cosmology as well as for theoretically motivated models, such as $f (R)$ gravity and massive neutrinos. For the majority of cosmologies we have tested, the emulator can reproduce the matter power spectrum with errors $lesssim 1%$ deep into the highly non-linear regime. This work demonstrates that with a well-designed suite of $Lambda$CDM simulations, extensions to the standard cosmological model can be tested in the non-linear regime without any reliance on expensive beyond-$Lambda$CDM simulations.
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