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 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 combine data from a number of N‐body simulations to predict the abundance of dark haloes in cold dark matter (CDM) universes over more than four orders of magnitude in mass. A comparison of different simulations suggests that the dominant uncertainty in our results is systematic and is smaller than 10–30 per cent at all masses, depending on the halo definition used. In particular, our ‘Hubble volume’ simulations of τCDM and ΛCDM cosmologies allow the abundance of massive clusters to be predicted with uncertainties well below those expected in all currently planned observational surveys. We show that for a range of CDM cosmologies and for a suitable halo definition, the simulated mass function is almost independent of epoch, of cosmological parameters and of the initial power spectrum when expressed in appropriate variables. This universality is of exactly the kind predicted by the familiar Press–Schechter model, although this model predicts a mass function shape that differs from our numerical results, overestimating the abundance of ‘typical’ haloes and underestimating that of massive systems.

We introduce the Making Galaxies in a Cosmological Context (MaGICC) program of smoothed particle hydrodynamics (SPH) simulations. We describe a parameter study of galaxy formation simulations of an L ⋆ galaxy that uses early stellar feedback combined with supernova feedback to match the stellar mass-halo mass relationship. While supernova feedback alone can reduce star formation enough to match the stellar mass-halo mass relationship, the galaxy forms too many stars before z = 2 to match the evolution seen using abundance matching. Our early stellar feedback is purely thermal and thus operates like a UV ionization source as well as providing some additional pressure from the radiation of massive, young stars. The early feedback heats gas to > 10 6 K before cooling to 10 4 K. The pressure from this hot gas creates a more extended disk and prevents more star formation prior to z = 1 than supernovae feedback alone. The resulting disk galaxy has a flat rotation curve, an exponential surface brightness profile, and matches a wide range of disk scaling relationships. The disk forms from the inside-out with an increasing exponential scale length as the galaxy evolves. Overall, early stellar feedback helps to simulate galaxies that match observational results at low and high redshifts.

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.