We investigate the properties of dark matter haloes and subhaloes in an $f(R)$ gravity model with $|f_{R0}|=10^{-6}$, using a very high-resolution N-body simulation. The model is a borderline between being cosmologically interesting and yet still con
sistent with current data. We find that the halo mass function in this model has a maximum 20% enhancement compared with the $Lambda$CDM predictions between $z=1$ and $z=0$. Because of the chameleon mechanism which screens the deviation from standard gravity in dense environments, haloes more massive than $10^{13}h^{-1}M_odot$ in this $f(R)$ model have very similar properties to haloes of similar mass in $Lambda$CDM, while less massive haloes, such as that of the Milky Way, can have steeper inner density profiles and higher velocity dispersions due to their weaker screening. The halo concentration is remarkably enhanced for low-mass haloes in this model due to a deepening of the total gravitational potential. Contrary to the naive expectation, the halo formation time $z_f$ is later for low-mass haloes in this model, a consequence of these haloes growing faster than their counterparts in $Lambda$CDM at late times and the definition of $z_f$. Subhaloes, especially those less massive than $10^{11}h^{-1}M_odot$, are substantially more abundant in this $f(R)$ model for host haloes less massive than $10^{13}h^{-1}M_odot$. We discuss the implications of these results for the Milky Way satellite abundance problem. Although the overall halo and subhalo properties in this borderline $f(R)$ model are close to their $Lambda$CDM predictions, our results suggest that studies of the Local Group and astrophysical systems, aided by high-resolution simulations, can be valuable for further tests of it.
We introduce the idea of {it effective} dark matter halo catalog in $f(R)$ gravity, which is built using the {it effective} density field. Using a suite of high resolution N-body simulations, we find that the dynamical properties of halos, such as th
e distribution of density, velocity dispersion, specific angular momentum and spin, in the effective catalog of $f(R)$ gravity closely mimic those in the $Lambda$CDM model. Thus, when using effective halos, an $f(R)$ model can be viewed as a $Lambda$CDM model. This effective catalog therefore provides a convenient way for studying the baryonic physics, the galaxy halo occupation distribution and even semi-analytical galaxy formation in $f(R)$ cosmologies.
We reexamine the screening mechanism in $f(R)$ gravity using N-body simulations. By explicitly examining the relation between the extra scalar field $delta f_R$ and the gravitational potential $phi$ in the perturbed Universe, we find that the relatio
n between these two fields plays an important role in understanding the screening mechanism. We show that the screening mechanism in $f(R)$ gravity depends mainly on the depth of the potential well, and find a useful condition for identifying unscreened halos in simulations. We also discuss the potential application of our results to real galaxy surveys.
We analyse modelling techniques for the large-scale structure formed in scalar-tensor theories of constant Brans-Dicke parameter which match the concordance model background expansion history and produce a chameleon suppression of the gravitational m
odification in high-density regions. Thereby, we use a mass and environment dependent chameleon spherical collapse model, the Sheth-Tormen halo mass function and linear halo bias, the Navarro-Frenk-White halo density profile, and the halo model. Furthermore, using the spherical collapse model, we extrapolate a chameleon mass-concentration scaling relation from a LCDM prescription calibrated to N-body simulations. We also provide constraints on the model parameters to ensure viability on local scales. We test our description of the halo mass function and nonlinear matter power spectrum against the respective observables extracted from large-volume and high-resolution N-body simulations in the limiting case of f(R) gravity, corresponding to a vanishing Brans-Dicke parameter. We find good agreement between the two; the halo model provides a good qualitative description of the shape of the relative enhancement of the f(R) matter power spectrum with respect to LCDM caused by the extra attractive gravitational force but fails to recover the correct amplitude. Introducing an effective linear power spectrum in the computation of the two-halo term to account for an underestimation of the chameleon suppression at intermediate scales in our approach, we accurately reproduce the measurements from the N-body simulations.
We study the late-time Integrated Sachs-Wolfe (ISW) effect in $f(R)$ gravity using N-body simulations. In the $f(R)$ model under study, the linear growth rate is larger than that in general relativity (GR). This slows down the decay of the cosmic pot
ential and induces a smaller ISW effect on large scales. Therefore, the $dotPhi$ (time derivative of the potential) power spectrum at $k<0.1h$/Mpc is suppressed relative to that in GR. In the non-linear regime, relatively rapid structure formation in $f(R)$ gravity boosts the non-linear ISW effect relative to GR, and the $dotPhi$ power spectrum at $k>0.1h$/Mpc is increased (100$%$ greater on small scales at $z=0$). We explore the detectability of the ISW signal via stacking supercluster and supervoids. The differences in the corresponding ISW cold or hot spots are $sim 20%$ for structures of $sim 100$Mpc/$h$. Such differences are greater for smaller structures, but the amplitude of the signal is lower. The high amplitude of ISW signal detected by Granett et al. can not explained in the $f(R)$ model. We find relatively big differences between $f(R)$ and GR in the transverse bulk motion of matter, and discuss its detectability via the relative frequency shifts of photons from multiple lensed images.
There is growing interest in testing alternative gravity theories using the subtle gravitational redshifts in clusters of galaxies. However, current models all neglect a transverse Doppler redshift of similar magnitude, and some models are not self-c
onsistent. An equilibrium model would fix the gravitational and transverse Doppler velocity shifts to be about 6sigma^2/c and 3sigma^2/2c in order to fit the observed velocity dispersion sigma self-consistently. This result comes from the Virial Theorem for a spherical isotropic cluster, and is insensitive to the theory of gravity. A gravitational redshift signal also does not directly distinguish between the Einsteinian and f(R) gravity theories, because each theory requires different dark halo mass function to keep the clusters in equilibrium. When this constraint is imposed, the gravitational redshift has no sensitivity to theory. Indeed our N-body simulations show that the halo mass function differs in f(R), and that the transverse Doppler effect is stronger than analytically predicted due to non-equilibrium.
We study the matter and velocity divergence power spectra in a f(R) gravity theory and their time evolution measured from several large-volume N-body simulations with varying box sizes and resolution. We find that accurate prediction of the matter po
wer spectrum in f(R) gravity places stronger requirements on the simulation than is the case with LCDM, because of the nonlinear nature of the fifth force. Linear perturbation theory is shown to be a poor approximation for the f(R) models, except when the chameleon effect is very weak. We show that the relative differences from the fiducial LCDM model are much more pronounced in the nonlinear tail of the velocity divergence power spectrum than in the matter power spectrum, which suggests that future surveys which target the collection of peculiar velocity data will open new opportunities to constrain modified gravity theories. A close investigation of the time evolution of the power spectra shows that there is a pattern in the evolution history, which can be explained by the properties of the chameleon-type fifth force in f(R) gravity. Varying the model parameter |f_R0|, which quantifies the strength of the departure from standard gravity, mainly varies the epoch marking the onset of the fifth force, as a result of which the different f(R) models are in different stages of the same evolutionary path at any given time
We derive a simple analytical expression for the two-body force in a sub-class of MOND-like theories and make testable predictions in the modification to the two-body orbital period, shape, and precession rate, and escape speed etc. We demonstrate th
e applications of the modified Keplers law in the timing of satellite orbits around the Milky Way, and checking the feasibility of MOND in the orbit of Large Magellanic Cloud, the M31 galaxy, and the merging Bullet Clusters. MOND appears to be consistent with satellite orbits although with a tight margin. Our results on two-bodies are also generalized to restricted three-body, many-body problems, rings and shells.
Empirical theories of Dark Matter like MOND gravity and of Dark Energy like f(R) gravity were motivated by astronomical data. But could these theories be branches rooted from a more general hence natural framework? Here we propose the natural Lagrang
ian of such a framework based on simple dimensional analysis and co-variant symmetry requirements, and explore various outcomes in a top-down fashion. Our framework preserves the co-variant formulation of GR, but allows the expanding physical metric be bent by a single new species of Dark Fluid flowing in space-time. Its non-uniform stress tensor and current vector are simply functions of a vector field of variable norm, resembling the 4-vector electromagnetic potential description for the photon fluid, but is dark (e.g., by very early decoupling from the baryon-radiation fluid). The Dark Fluid framework naturally branches into a continuous spectrum of theories with Dark Energy and Dark Matter effects, including the $f(R)$ gravity, TeVeS-like theories, Einstein-Aether and $ uLambda$ theories as limiting cases. When the vector field degenerates into a pure Higgs-like scalar field, we obtain the physics for inflaton and quintessence. In this broad setting we emphasize the non-constant dynamical field behind the cosmological constant effect, and highlight plausible corrections beyond the classical MOND predictions. Choices of parameters can be made to pass BBN, PPN, and causality constraints. The Dark Fluid is inspired to unify/simplify the astronomically successful ingredients of previous constructions: the desired effects of inflaton plus quintessence plus Cold DM particle fields or MOND-like scalar field(s) are shown largely achievable by one vector field only.
