The cold dark matter model has become the leading theoretical picture for the formation of structure in the Universe. This model, together with the theory of cosmic inflation, makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a simulation of the growth of dark matter structure using 2,160(3) particles, following them from redshift z = 127 to the present in a cube-shaped region 2.230 billion lightyears on a side. In postprocessing, we also follow the formation and evolution of the galaxies and quasars. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with future generations of observational surveys of galaxies.

We introduce the Virgo Consortium's EAGLE project, a suite of hydrodynamical simulations that follow the formation of galaxies and supermassive black holes in cosmologically representative volumes of a standard ΛCDM universe. We discuss the limitations of such simulations in light of their finite resolution and poorly constrained subgrid physics, and how these affect their predictive power. One major improvement is our treatment of feedback from massive stars and AGN in which thermal energy is injected into the gas without the need to turn off cooling or decouple hydrodynamical forces, allowing winds to develop without predetermined speed or mass loading factors. Because the feedback efficiencies cannot be predicted from first principles, we calibrate them to the present-day galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy stellar mass function is reproduced to < ∼ 0.2 dex over the full resolved mass range, 10 8 < M * /M < ∼ 10 11 , a level of agreement close to that attained by semi-analytic models, and unprecedented for hydrodynamical simulations. We compare our results to a representative set of low-redshift observables not considered in the calibration, and find good agreement with the observed galaxy specific star formation rates, passive fractions, Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic C iv and O vi. While the mass-metallicity relations for gas and stars are consistent with observations for M * > ∼ 10 9 M (M * > ∼ 10 10 M at intermediate resolution), they are insufficiently steep at lower masses. For the reference model the gas fractions and temperatures are too high for clusters of galaxies, but for galaxy groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. The EAGLE simulation suite, which also includes physics variations and higher-resolution zoomed-in volumes described elsewhere, constitutes a valuable new resource for studies of galaxy formation.

We present the results of a large library of cosmological N‐body simulations, using power‐law initial spectra. The non‐linear evolution of the matter power spectra is compared with the predictions of existing analytic scaling formulae based on the work of Hamilton et al. The scaling approach has assumed that highly non‐linear structures obey ‘stable clustering’ and are frozen in proper coordinates. Our results show that, when transformed under the self‐similarity scaling, the scale‐free spectra define a non‐linear locus that is clearly shallower than would be required under stable clustering. Furthermore, the small‐scale non‐linear power increases as both the power spectrum index n and the density parameter Ω decrease, and this evolution is not well accounted for by the previous scaling formulae. This breakdown of stable clustering can be understood as resulting from the modification of dark matter haloes by continuing mergers. These effects are naturally included in the analytic ‘halo model’ for non‐linear structure; we use this approach to fit both our scale‐free results and also our previous cold dark matter data. This method is more accurate than the commonly used Peacock–Dodds formula and should be applicable to more general power spectra. Code to evaluate non‐linear power spectra using this method is available from http://as1.chem.nottingham.ac.uk/~res/software.html. Following publication, we will make the power‐law simulation data publically available through the Virgo website http://www.mpa-garching.mpg.de/Virgo/.

We have updated the Munich galaxy formation model to the Planck first-year cosmology, while modifying the treatment of baryonic processes to reproduce recent data on the abundance and passive fractions of galaxies from z = 3 down to z = 0. Matching these more extensive and more precise observational results requires us to delay the reincorporation of wind ejecta, to lower the surface density threshold for turning cold gas into stars, to eliminate ram-pressure stripping in haloes less massive than ∼ 10 14 M ⊙ , and to modify our model for radio mode feedback. These changes cure the most obvious failings of our previous models, namely the overly early formation of low-mass galaxies and the overly large fraction of them that are passive at late times. The new model is calibrated to reproduce the observed evolution both of the stellar mass function and of the distribution of star formation rate at each stellar mass. Massive galaxies (log M * / M ⊙ 11.0) assemble most of their mass before z = 1 and are predominantly old and passive at z = 0, while lower mass galaxies assemble later and, for log M * / M ⊙ 9.5, are still predominantly blue and star forming at z = 0. This phenomenological but physically based model allows the observations to be interpreted in terms of the efficiency of the various processes that control the formation and evolution of galaxies as a function of their stellar mass, gas content, environment and time.

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including SPH and grid methods with fixed, deformable or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gas dynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of two. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to about 10%, and the ratio of specific kinetic to thermal energies of the gas agree to about 5%. Various factors contribute to the spread in calculated cluster properties, including differences in the internal timing of the simulations. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modelled.