Wojciech A. Hellwing

The non-linear matter and velocity power spectra in f(R) gravity

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 power spectrum in f(R) gravity places stronger requirements on the simulation than is the case with Λ cold dark matter (ΛCDM) because of the non-linear 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 ΛCDM model are much more pronounced in the non-linear 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 |fR0|, 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.

Nonlinear structure formation in the cubic Galileon gravity model

We model the linear and nonlinear growth of large scale structure in the Cubic Galileon gravity model, by running a suite of N-body cosmological simulations using the ECOSMOG code. Our simulations include the Vainshtein screening effect, which reconciles the Cubic Galileon model with local tests of gravity. In the linear regime, the amplitude of the matter power spectrum increases by ~ 20% with respect to the standard ΛCDM model today. The modified expansion rate accounts for ~ 15% of this enhancement, while the fifth force is responsible for only ~ 5%. This is because the effective unscreened gravitational strength deviates from standard gravity only at late times, even though it can be twice as large today. In the nonlinear regime (k0.1h Mpc−1), the fifth force leads to only a modest increase (8%) in the clustering power on all scales due to the very efficient operation of the Vainshtein mechanism. Such a strong effect is typically not seen in other models with the same screening mechanism. The screening also results in the fifth force increasing the number density of halos by less than 10%, on all mass scales. Our results show that the screening does not ruin the validity of linear theory on large scales which anticipates very strong constraints from galaxy clustering data. We also show that, whilst the model gives an excellent match to CMB data on small angular scales (l50), the predicted integrated Sachs-Wolfe effect is in tension with Planck/WMAP results.

The mass–concentration–redshift relation of cold and warm dark matter haloes.

We use a suite of cosmological simulations to study the mass–concentration–redshift relation, c(M, z), of dark matter haloes. Our simulations include standard Λ-cold dark matter (CDM) models, and additional runs with truncated power spectra, consistent with a thermal warm dark matter (WDM) scenario. We find that the mass profiles of CDM and WDM haloes are self-similar and well approximated by the Einasto profile. The c(M, z) relation of CDM haloes is monotonic: concentrations decrease with increasing virial mass at fixed redshift, and decrease with increasing redshift at fixed mass. The mass accretion histories (MAHs) of CDM haloes are also scale-free, and can be used to infer concentrations directly. These results do not apply to WDM haloes: their MAHs are not scale-free because of the characteristic scale imposed by the power spectrum suppression. Further, the WDM c(M, z) relation is non-monotonic: concentrations peak at a mass scale dictated by the truncation scale, and decrease at higher and lower masses. We show that the assembly history of a halo can still be used to infer its concentration, provided that the total mass of its progenitors is considered (the ‘collapsed mass history’; CMH), rather than just that of its main ancestor. This exploits the scale-free nature of CMHs to derive a simple scaling that reproduces the mass–concentration–redshift relation of both CDM and WDM haloes over a vast range of halo masses and redshifts. Our model therefore provides a robust account of the mass, redshift, cosmology and power spectrum dependence of dark matter halo concentrations.

Simulating the quartic Galileon gravity model on adaptively refined meshes

We develop a numerical algorithm to solve the high-order nonlinear derivative-coupling equation associated with the quartic Galileon model, and implement it in a modified version of the ramses N-body code to study the effect of the Galileon field on the large-scale matter clustering. The algorithm is tested for several matter field configurations with different symmetries, and works very well. This enables us to perform the first simulations for a quartic Galileon model which provides a good fit to the cosmic microwave background (CMB) anisotropy, supernovae and baryonic acoustic oscillations (BAO) data. Our result shows that the Vainshtein mechanism in this model is very efficient in suppressing the spatial variations of the scalar field. However, the time variation of the effective Newtonian constant caused by the curvature coupling of the Galileon field cannot be suppressed by the Vainshtein mechanism. This leads to a significant weakening of the strength of gravity in high-density regions at late times, and therefore a weaker matter clustering on small scales. We also find that without the Vainshtein mechanism the model would have behaved in a completely different way, which shows the crucial role played by nonlinearities in modified gravity theories and the importance of performing self-consistent N-body simulations for these theories.

Nonlinear Structure Formation in Nonlocal Gravity

We now turn our attention to large scale structure formation in nonlocal gravity models. In these models, the modifications to gravity arise via the addition of nonlocal terms (i.e. which depend on more than one point in spacetime) to the Einstein field equations. These terms typically involve the inverse of the d’Alembertian operator, \(\Box ^{-1}\), acting on curvature tensors.

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. (2014a) and Boyarsky et al. (2014a) 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 13:4bn particles, each of mass 10 5 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 10 9 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 10 9 h 1 M and declines very rapidly towards lower masses so that there are five times fewer haloes of mass M200 = 10 8 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.

The Copernicus Complexio: a high-resolution view of the small-scale Universe

We introduce Copernicus Complexio (COCO), a high-resolution cosmological N-body simulation of structure formation in the ΛCDM model. COCO follows an approximately spherical region of radius ∼17.4 h−1 Mpc embedded in a much larger periodic cube that is followed at lower resolution. The high-resolution volume has a particle mass of 1.135 × 105 h−1 M⊙ (60 times higher than the Millennium-II simulation). COCO gives the dark matter halo mass function over eight orders of magnitude in halo mass; it forms ∼60 haloes of galactic size, each resolved with about 10 million particles. We confirm the power-law character of the subhalo mass function, , down to a reduced subhalo mass Msub/M200 ≡ μ = 10−6, with a best-fitting power-law index, s = 0.94, for hosts of mass 〈M200〉 = 1012 h−1 M⊙. The concentration–mass relation of COCO haloes deviates from a single power law for masses M200 < afew × 108 h−1 M⊙, where it flattens, in agreement with results by Sanchez-Conde et al. The host mass invariance of the reduced maximum circular velocity function of subhaloes, ν ≡ Vmax/V200, hinted at in previous simulations, is clearly demonstrated over five orders of magnitude in host mass. Similarly, we find that the average, normalized radial distribution of subhaloes is approximately universal (i.e. independent of subhalo mass), as previously suggested by the Aquarius simulations of individual haloes. Finally, we find that at fixed physical subhalo size, subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts.

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.

Modified Gravity N-body Code Comparison Project

Self-consistent N-body simulations of modified gravity models are a key ingredient to obtain rigorous constraints on deviations from general relativity using large-scale structure observations. This paper provides the first detailed comparison of the results of different N-body codes for the f (R), Dvali-Gabadadze-Porrati and Symmetron models, starting from the same initial conditions. We find that the fractional deviation of the matter power spectrum from Lambda cold dark matter agrees to better than 1 per cent up to k ˜ 5-10 h Mpc-1 between the different codes. These codes are thus able to meet the stringent accuracy requirements of upcoming observational surveys. All codes are also in good agreement in their results for the velocity divergence power spectrum, halo abundances and halo profiles. We also test the quasi-static limit, which is employed in most modified gravity N-body codes, for the Symmetron model for which the most significant non-static effects among the models considered are expected. We conclude that this limit is a very good approximation for all of the observables considered here.

Dark matter gravitational clustering with a long-range scalar interaction

We explore the possibility of improving the {lambda}CDM model at megaparsec scales by introducing a scalar interaction that increases the mutual gravitational attraction of dark matter particles. Using N-body simulations, we study the spatial distribution of dark matter particles and halos. We measure the effect of modifications in the Newtons gravity on properties of the two-point correlation function, the dark matter power spectrum, the cumulative halo mass function, and density probability distribution functions. The results look promising: the scalar interactions produce desirable features at megaparsec scales without spoiling the {lambda}CDM successes at larger scales.