Testing the quasi-static approximation in f(R) gravity simulations

Numerical simulations in modified gravity have commonly been performed under the quasi-static approximation—that is, by neglecting the effect of time derivatives in the equation of motion of the scalar field that governs the fifth force in a given modified gravity theory. To test the validity of this approximation, we analyse the case of f(R) gravity beyond this quasi-static limit, by considering effects, if any, these terms have in the matter and velocity divergence cosmic fields. To this end, we use the adaptive mesh refinement code ECOSMOG to study three variants (|fR|= 10−4[F4], 10−5[F5] and 10−6[F6]) of the Hu-Sawicki f(R) gravity model, each of which refers to a different magnitude for the scalar field that generates the fifth force. We find that for F4 and F5, which show stronger deviations from standard gravity, a low-resolution simulation is enough to conclude that time derivatives make a negligible contribution to the matter distribution. The F6 model shows a larger deviation from the quasi-static approximation, but one that diminishes when re-simulated at higher-resolution. We therefore come to the conclusion that the quasi-static approximation is valid for the most practical applications in f(R) cosmologies

Exploring the liminality: properties of haloes and subhaloes in borderline f(R) gravity

We investigate the properties of dark matter haloes and subhaloes in an f(R) gravity model with |fR0| = 10−6, using a very-high-resolution N-body simulation. The model is a borderline between being cosmologically interesting and yet still consistent with current data. We find that the halo mass function in this model has a maximum 20 per cent enhancement compared with the Λ-cold-dark-matter (ΛCDM) predictions between z = 1 and 0. Because of the chameleon mechanism which screens the deviation from standard gravity in dense environments, haloes more massive than 1013 h−1 M⊙ in this f(R) model have very similar properties to haloes of similar mass in ΛCDM, 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 zf is later for low-mass haloes in this model, a consequence of these haloes growing faster than their counterparts in ΛCDM at late times and the definition of zf. Subhaloes, especially those less massive than 1011 h−1 M⊙, are substantially more abundant in this f(R) model for host haloes less massive than 1013 h−1 M⊙. 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 ΛCDM 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

Clear and measurable signature of modified gravity in the galaxy velocity field

The velocity field of dark matter and galaxies reflects the continued action of gravity throughout cosmic history. We show that the low-order moments of the pairwise velocity distribution, v 12 , are a powerful diagnostic of the laws of gravity on cosmological scales. In particular, the projected line-of-sight galaxy pairwise velocity dispersion, σ 12 (r) , is very sensitive to the presence of modified gravity. Using a set of high-resolution N-body simulations we compute the pairwise velocity distribution and its projected line-of-sight dispersion for a class of modified gravity theories: the chameleon f(R) gravity and Galileon gravity (cubic and quartic). The velocities of dark matter halos with a wide range of masses exhibit deviations from General Relativity at the 5 to 10 σ level. We examine strategies for detecting these deviations in galaxy redshift and peculiar velocity surveys. If detected, this signature would be a smoking gun for modified gravity

Nonlinear structure formation in Nonlocal Gravity

We study the nonlinear growth of structure in nonlocal gravity models with the aid of N-body simulation and the spherical collapse and halo models. We focus on a model in which the inverse-squared of the d'Alembertian operator acts on the Ricci scalar in the action. For fixed cosmological parameters, this model differs from ΛCDM by having a lower late-time expansion rate and an enhanced and time-dependent gravitational strength ~ 6% larger today). Compared to ΛCDM today, in the nonlocal model, massive haloes are slightly more abundant (by ~ 10% at M ~ 1014 M⊙/h) and concentrated ≈ 8% enhancement over a range of mass scales), but their linear bias remains almost unchanged. We find that the Sheth-Tormen formalism describes the mass function and halo bias very well, with little need for recalibration of free parameters. The fitting of the halo concentrations is however essential to ensure the good performance of the halo model on small scales. For k gsim 1 h/Mpc, the amplitude of the nonlinear matter and velocity divergence power spectra exhibits a modest enhancement of ~ 12% to 15%, compared to ΛCDM today. This suggests that this model might only be distinguishable from ΛCDM by future observational missions. We point out that the absence of a screening mechanism may lead to tensions with Solar System tests due to local time variations of the gravitational strength, although this is subject to assumptions about the local time evolution of background averaged quantities

Subhalo statistics of galactic haloes: beyond the resolution limit

We study the substructure population of Milky Way (MW)-mass haloes in the Λ cold dark matter (ΛCDM) cosmology using a novel procedure to extrapolate subhalo number statistics beyond the resolution limit of N-body simulations. The technique recovers the mean and the variance of the subhalo abundance, but not its spatial distribution. It extends the dynamic range over which precise statistical predictions can be made by the equivalent of performing a simulation with 50 times higher resolution, at no additional computational cost. We apply this technique to MW-mass haloes, but it can easily be applied to haloes of any mass. We find up to 20 per cent more substructures in MW-mass haloes than found in previous studies. Our analysis lowers the mass of the MW halo required to accommodate the observation that the MW has only three satellites with a maximum circular velocity Vmax ≥ 30 km s− 1 in the ΛCDM cosmology. The probability of having a subhalo population similar to that in the MW is 20 per cent for a virial mass, M200 = 1 × 1012 M⊙ and practically zero for haloes more massive than M200 = 2 × 1012 M⊙

The effect of baryons on redshift space distortions and cosmic density and velocity fields in the EAGLE simulation

We use the Evolution and Assembly of GaLaxies and their Environments (EAGLE) galaxy formation simulation to study the effects of baryons on the power spectrum of the total matter and dark matter distributions and on the velocity fields of dark matter and galaxies. On scales k ≳ 4 h Mpc−1 the effect of baryons on the amplitude of the total matter power spectrum is greater than 1 per cent. The back-reaction of baryons affects the density field of the dark matter at the level of ∼3 per cent on scales of 1 ≤ k/( h Mpc−1) ≤ 5. The dark matter velocity divergence power spectrum at k ≲ 0.5 h Mpc−1 is changed by less than 1 per cent. The 2D redshift space power spectrum is affected at the level of ∼6 per cent at |k|≳1hMpc−1|k|≳1hMpc−1 (for μ > 0.5), but for |k|≤0.4hMpc−1|k|≤0.4hMpc−1 it differs by less than 1 per cent. We report vanishingly small baryonic velocity bias for haloes: the peculiar velocities of haloes with M200 > 3 × 1011 M⊙ (hosting galaxies with M* > 109 M⊙) are affected at the level of at most 1 km s−1, which is negligible for 1 per cent-precision cosmology. We caution that since EAGLE overestimates cluster gas fractions it may also underestimate the impact of baryons, particularly for the total matter power spectrum. Nevertheless, our findings suggest that for theoretical modelling of redshift space distortions and galaxy velocity-based statistics, baryons and their back-reaction can be safely ignored at the current level of observational accuracy. However, we confirm that the modelling of the total matter power spectrum in weak lensing studies needs to include realistic galaxy formation physics in order to achieve the accuracy required in the precision cosmology era

The Copernicus Complexio: Statistical Properties of Warm Dark Matter Haloes

The recent detection of a 3.5 keV X-ray line from the centres of galaxies and clusters by Bulbul et al. and Boyarsky et al. has been interpreted as emission from the decay of 7 keV sterile neutrinos which could make up the (warm) dark matter (WDM). As part of the Copernicus Complexio (COCO) programme, we investigate the properties of dark matter haloes formed in a high-resolution cosmological N-body simulation from initial conditions similar to those expected in a universe in which the dark matter consists of 7 keV sterile neutrinos. This simulation and its cold dark matter (CDM) counterpart have ∼13.4 bn particles, each of mass ∼105 h−1 M⊙, providing detailed information about halo structure and evolution down to dwarf galaxy mass scales. Non-linear structure formation on small scales (M200 ≲ 2 × 109 h−1 M⊙) begins slightly later in COCO-WARM than in COCO-COLD. The halo mass function at the present day in the WDM model begins to drop below its CDM counterpart at a mass ∼2 × 109 h−1 M⊙ and declines very rapidly towards lower masses so that there are five times fewer haloes of mass M200 = 108 h−1 M⊙ in COCO-WARM than in COCO-COLD. Halo concentrations on dwarf galaxy scales are correspondingly smaller in COCO-WARM, and we provide a simple functional form that describes its evolution with redshift. The shapes of haloes are similar in the two cases, but the smallest haloes in COCO-WARM rotate slightly more slowly than their CDM counterparts

Planes of satellite galaxies: when exceptions are the rule

The detection of planar structures within the satellite systems of both the Milky Way (MW) and Andromeda (M31) has been reported as being in stark contradiction to the predictions of the standard cosmological model (Λ cold dark matter – ΛCDM). Given the ambiguity in defining a planar configuration, it is unclear how to interpret the low incidence of the MW and M31 planes in ΛCDM. We investigate the prevalence of satellite planes around galactic mass haloes identified in high-resolution cosmological simulations. We find that planar structures are very common, and that ∼10 per cent of ΛCDM haloes have even more prominent planes than those present in the Local Group. While ubiquitous, the planes of satellite galaxies show a large diversity in their properties. This precludes using one or two systems as small-scale probes of cosmology, since a large sample of satellite systems is needed to obtain a good measure of the object-to-object variation. This very diversity has been misinterpreted as a discrepancy between the satellite planes observed in the Local Group and ΛCDM predictions. In fact, ∼10 per cent of ΛCDM galactic haloes have planes of satellites that are as infrequent as the MW and M31 planes. The look-elsewhere effect plays an important role in assessing the detection significance of satellite planes and accounting for it leads to overestimating the significance level by a factor of 30 and 100 for the MW and M31 systems, respectively

Nexus of the cosmic web.

One of the important unknowns of current cosmology concerns the effects of the large scale distribution of matter on the formation and evolution of dark matter haloes and galaxies. One main difficulty in answering this question lies in the absence of a robust and natural way of identifying the large scale environments and their characteristics. This work summarizes the NEXUS+ formalism which extends and improves our multiscale scale-space MMF method. The new algorithm is very successful in tracing the Cosmic Web components, mainly due to its novel filtering of the density in logarithmic space. The method, due to its multiscale and hierarchical character, has the advantage of detecting all the cosmic structures, either prominent or tenuous, without preference for a certain size or shape. The resulting filamentary and wall networks can easily be characterized by their direction, thickness, mass density and density profile. These additional environmental properties allows to us to investigate not only the effect of environment on haloes, but also how it correlates with the environment characteristics