The Hubble flow around the Local Group

We use updated data on distances and velocities of galaxies in the proximity of the Local Group (LG) in order to establish properties of the local Hubble flow. For 30 neighbouring galaxies with distances  0.7 < D _LG < 3.0  Mpc, the local flow is characterized by the Hubble parameter   H _loc= (78 ± 2) km s⁻¹ Mpc⁻¹  , the mean-square peculiar velocity  σ_v= 25 km s⁻¹  , corrected for errors of radial velocity measurements  (∼4 km s⁻¹)  and distance measurements  (∼10 km s⁻¹)  , as well as the radius of the zero-velocity surface   R ₀= (0.96 ± 0.03)  Mpc. The minimum value for σ_v is achieved when the barycentre of the LG is located at the distance   D_c = (0.55 ± 0.05) D _M31  towards Andromeda galaxy (M31) corresponding to the Milky Way (MW)-to-M31 mass ratio   M _MW/ M _M31≃ 4/5  . In the reference frame of the 30 galaxies at 0.7–3.0 Mpc, the LG barycentre has a small peculiar velocity  ∼(24 ± 4) km s⁻¹  towards the Sculptor constellation. The derived value of R ₀ corresponds to the total mass   M _T(LG) = (1.9 ± 0.2) 10¹² M_⊙  with  Ω_m= 0.24  and a topologically flat universe, a value in good agreement with the sum of virial mass estimates for the MW and M31.     

Voids in a ΛCDM universe

We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular Λ cold dark matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of −0.8 or less – roughly the equivalent of using a spherical overdensity group finder for haloes. Each of the simulations contains thousands of voids. The distribution of void sizes in the different simulations shows good agreement when differences in particle and grid resolution are accounted for. Voids very clearly correspond to minima in the smoothed initial density field. Apart from a very weak dependence on the mass resolution, the rescaled mass profiles of voids in the different simulations agree remarkably well. We find a universal void mass profile of the form  ρ(< r )/ρ( r _eff) ∝ exp[( r / r _eff)^α]  , where r _eff is the effective radius of a void and  α∼ 2  . The mass function of haloes in voids is steeper than that of haloes that populate denser regions. In addition, the abundances of void haloes seem to evolve somewhat more strongly between redshifts ∼1 and 0 than the global abundances of haloes.     

The signature of dark energy on the local Hubble flow

Using N -body simulations of flat, dark energy-dominated cosmologies, we show that galaxies around simulated binary systems resembling the Local Group (LG) have low peculiar velocities, in good agreement with observational data. We have compared results for LG-like systems selected from large, high-resolution simulations of three cosmologies: a ΛCDM model, a ΛWDM model with a 2-keV warm dark matter candidate, and a quintessence (QCDM) model with an equation-of-state parameter   w =−0.6  . The Hubble flow is significantly colder around LGs selected in a flat, Λ-dominated cosmology than around LGs in open or critical models, showing that a dark energy component manifests itself on the scales of nearby galaxies, cooling galaxy peculiar motions. Flows in the ΛWDM and QCDM models are marginally colder than in the ΛCDM one.
The results of our simulations have been compared to existing data and to a new data set of 28 nearby galaxies with robust distance measures (Cepheids and surface brightness fluctuations). The measured line-of-sight velocity dispersion is given by  σ_H= (88 ± 20  km s⁻¹) × ( R /7 Mpc)  . The best agreement with observations is found for LGs selected in the ΛCDM cosmology in environments with  −0.1 < δρ/ρ < 0.6  on scales of 7 Mpc, in agreement with existing observational estimates on the local matter density. These results provide new, independent evidence for the presence of dark energy on scales of a few megaparsecs, corroborating the evidence gathered from observations of distant objects and the early Universe.     

Power spectrum for the small-scale Universe

The first objects to arise in a cold dark matter (CDM) universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution  ( N = 720³–1584³)  simulations of an Einstein–de Sitter cosmology where the initial power spectrum is   P ( k ) ∝ k ⁿ ,  with  −2.5 ≤ n ≤− 1  . Self-similar scaling is established for   n =−1  and −2 more convincingly than in previous, lower resolution simulations and for the first time, self-similar scaling is established for an   n =−2.25  simulation. However, finite box-size effects induce departures from self-similar scaling in our   n =−2.5  simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasi-linear regime. In the non-linear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis versus halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high- k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.     

The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, ξ and ζ , in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10  h ⁻¹ Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function   Q ₃∼ ζ / ξ ²  . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ≃20 Mpc  h ⁻¹. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading-order PT become important at smaller scales   r ≃10 Mpc  h ^-1  , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.