▪ Abstract Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below ao ≈ 10−8 cm/s2 ≈ cHo/6 the effective gravitational attraction approaches , where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ∝ V4 that forms the basis for the observed luminosity–rotation velocity relation—the Tully-Fisher law. We review the phenomenological success of MOND on scales ranging from dwarf spheroidal galaxies to superclusters and demonstrate that the evidence for dark matter can be equally well interpreted as evidence for MOND. We discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics as well as the extention of MOND to cosmology and structure formation.

We use the halo model of clustering to compute two- and three-point correlation functions for weak lensing, and apply them in a new statistical technique to measure properties of massive haloes. We present analytical results on the eight shear three-point correlation functions constructed using a combination of the two shear components at each vertex of a triangle. We compare the amplitude and configuration dependence of the functions with ray-tracing simulations and find excellent agreement for different scales and models. These results are promising, since shear statistics are easier to measure than the convergence. In addition, the symmetry properties of the shear three-point functions provide a new and precise way of disentangling the lensing E mode from the B mode due to possible systematic errors. We develop an approach based on correlation functions to measure the properties of galaxy-group and cluster haloes from lensing surveys. Shear correlations on small scales arise from the lensing matter within haloes of mass M ? 10 1 3 M O .. Thus, the measurement of two- and three-point correlations can be used to extract information on halo density profiles, primarily the inner slope and halo concentration. We demonstrate the feasibility of such an analysis for forthcoming surveys. We include covariances in the correlation functions due to sample variance and intrinsic ellipticity noise to show that 10 per cent accuracy on profile parameters is achievable with surveys such as the CFHT Legacy survey, and significantly better with future surveys. Our statistical approach is complementary to the standard approach of identifying individual objects in survey data and measuring their properties. It can be extended to perform a combined analysis of the large-scale, perturbative regime down to small, subarcminute scales, to obtain consistent measurements of cosmological parameters and halo properties.

We use the Millennium Simulation (MS) to measure the cross-correlation between halo centres and mass (or equivalently the average density profiles of dark haloes) in a Lambda cold dark matter (ACDM) cosmology. We present results for radii in the range 10 h -1 kpc < r < 30 h -1 Mpc and for halo masses in the range 4 x 10 10 < M 200 < 4 x 10 14 h -1 M ⊙ . Both at z = 0 and at z = 0.76 these cross-correlations are surprisingly well fitted if the inner region is approximated by a density profile of NFW or Einasto form, the outer region by a biased version of the linear mass autocorrelation function, and the maximum of the two is adopted where they are comparable. We use a simulation of galaxy formation within the MS to explore how these results are reflected in cross-correlations between galaxies and mass. These are directly observable through galaxy-galaxy lensing. Here also we find that simple models can represent the simulation results remarkably well, typically to ≤10 per cent. Such models can be used to extend our results to other redshifts, to cosmologies with other parameters, and to other assumptions about how galaxies populate dark haloes. Our galaxy formation simulation already reproduces current galaxy-galaxy lensing data quite well. The characteristic features predicted in the galaxy-galaxy lensing signal should provide a strong test of the ACDM cosmology as well as a route to understanding how galaxies form within it.

We use the LUQAS sample, a set of 27 high-resolution and high signal-to-noise ratio quasi-stellar object (QSO) absorption spectra at a median redshift of z = 2.25, and the data from Croft et al. at a median redshift of z = 2.72, together with a large suite of high-resolution large box-size hydrodynamical simulations, to estimate the linear dark matter power spectrum on scales 0.003 < k < 0.03 s km -1 . Our reanalysis of the Croft et al. data agrees well with their results if we assume the same mean optical depth and gas temperature-density relation. The inferred linear dark matter power spectrum at z = 2.72 also agrees with that inferred from LUQAS at lower redshift if we assume that the increase of the amplitude is due to gravitational growth between these redshifts. We further argue that the smaller mean optical depth measured from high-resolution spectra is more accurate than the larger value obtained from low-resolution spectra by Press et al. which Croft et al. used. For the smaller optical depth we obtain a 20 per cent higher value for the rms fluctuation amplitude of the matter density. By combining the amplitude of the matter power spectrum inferred from the Lya forest with the amplitude on large scales inferred from measurements of the CMB we obtain constraints on the primordial spectral index n and the normalization σ 8 . For values of the mean optical depth favoured by high-resolution spectra, the inferred linear power spectrum is consistent with a ACDM model with a scale-free (n = 1) primordial power spectrum.

We use seven high-resolution N-body simulations to study the correlations among different halo properties (assembly time, spin, shape and substructure), and how these halo properties are correlated with the large-scale environment in which haloes reside. The large-scale tidal field estimated from haloes above a mass threshold is used as our primary quantity to characterize the large-scale environment, while other parameters, such as the local overdensity and the morphology of large-scale structure, are used for comparison. For haloes at a fixed mass, all the halo properties depend significantly on environment, particularly the tidal field. The environmental dependence of halo assembly time is primarily driven by local tidal field. The mass of the unbound fraction in substructure is boosted in strong tidal force region, while the bound fraction is suppressed. Haloes have a tendency to spin faster in a stronger tidal field and the trend is stronger for more massive haloes. The spin vectors show significant alignment with the intermediate axis of the tidal field, as expected from the tidal torque theory. Both the major and minor axes of haloes are strongly aligned with the corresponding principal axes of the tidal field. In general, a halo that can accrete more material after the formation of its main halo on average is younger, more elongated, spins faster and contains a larger amount of substructure. Higher-density environments not only provide more material for haloes to accrete, but also are places of stronger tidal fields that tend to suppress halo accretion. The environmental dependencies are the results of these two competing effects. The tidal field based on haloes can be estimated from observation, and we discuss the implications of our results for the environmental dependence of galaxy properties.

We use numerical simulations to investigate, for the first time, the joint effect of feedback from supernovae (SNe) and active galactic nuclei (AGN) on the evolution of galaxy cluster X-ray scaling relations. Our simulations are drawn from the Millennium Gas Project and are some of the largest hydrodynamical N-body simulations ever carried out. Feedback is implemented using a hybrid scheme, where the energy input into intracluster gas by SNe and AGN is taken from a semi-analytic model of galaxy formation. This ensures that the source of feedback is a population of galaxies that closely resembles that found in the real Universe. We show that our feedback model is capable of reproducing observed local X-ray scaling laws, at least for non-cool-core clusters, but that almost identical results can be obtained with a simplistic preheating model. However, we demonstrate that the two models predict opposing evolutionary behaviour. We have examined whether the evolution predicted by our feedback model is compatible with observations of high-redshift clusters. Broadly speaking, we find that the data seem to favour the feedback model for z? 0.5, and the preheating model at higher redshift. However, a statistically meaningful comparison with observations is impossible, because the large samples of high-redshift clusters currently available are prone to strong selection biases. As the observational picture becomes clearer in the near future, it should be possible to place tight constraints on the evolution of the scaling laws, providing us with an invaluable probe of the physical processes operating in galaxy clusters.

We use numerical simulations of a (480 Mpc h−1)3 volume to show that the distribution of peak heights in maps of the temperature fluctuations from the kinematic and thermal Sunyaev–Zeldovich (SZ) effects will be highly non-Gaussian, and very different from the peak-height distribution of a Gaussian random field. We then show that it is a good approximation to assume that each peak in either SZ effect is associated with one and only one dark matter halo. This allows us to use our knowledge of the properties of haloes to estimate the peak-height distributions. At fixed optical depth, the distribution of peak heights resulting from the kinematic effect is Gaussian, with a width that is approximately proportional to the optical depth; the non-Gaussianity comes from summing over a range of optical depths. The optical depth is an increasing function of halo mass and the distribution of halo speeds is Gaussian, with a dispersion that is approximately independent of halo mass. This means that observations of the kinematic effect can be used to put constraints on how the abundance of massive clusters evolves, and on the evolution of cluster velocities. The non-Gaussianity of the thermal effect, on the other hand, comes primarily from the fact that, on average, the effect is larger in more massive haloes, and the distribution of halo masses is highly non-Gaussian. We also show that because haloes of the same mass may have a range of density and velocity dispersion profiles, the relation between halo mass and the amplitude of the thermal effect is not deterministic, but has some scatter.

We use gigaparticle N-body simulations to study galaxy cluster populations in Hubble volumes of ΛCDM (Ωm = 0.3, ΩΛ = 0.7) and τCDM (Ωm = 1) world models. Mapping past light cones of locations in the computational space, we create mock sky surveys of dark matter structure to z ≃ 1.4 over 10,000 deg2 and to z ≃ 0.5 over two full spheres. Calibrating the Jenkins mass function at z = 0 with samples of ~1.5 million clusters, we show that the fit describes the sky survey counts to ≲20% accuracy over all redshifts for systems more massive than poor galaxy groups (5 × 1013 h-1 M☉). Fitting the observed local temperature function determines the ratio β of specific thermal energies in dark matter and intracluster gas. We derive a scaling with power spectrum normalization β ∝ σ and find that the ΛCDM model requires σ8 = 1.04 to match β = 1.17 derived from gasdynamic cluster simulations. We estimate a 10% overall systematic uncertainty in σ8, 4% arising from cosmic variance in the local sample and the bulk from uncertainty in the absolute mass scale of clusters. Considering distant clusters, the ΛCDM model matches Extended Medium-Sensitivity Survey and ROSAT Deep Cluster Survey X-ray-selected observations under economical assumptions for intracluster gas evolution. Using transformations of mass-limited cluster samples that mimic σ8 variation, we explore Sunyaev-Zeldovich (SZ) search expectations for a 10 deg2 survey complete above 1014 h-1 M☉. Cluster counts are shown to be extremely sensitive to σ8 uncertainty, while redshift statistics, such as the sample median, are much more stable. Redshift information is crucial to extract the full cosmological diagnostic power of SZ cluster surveys. For ΛCDM, the characteristic temperature at a fixed sky surface density is a weak function of redshift, implying an abundance of hot clusters at z > 1. Assuming constant β, one 8 keV cluster at z > 2 and 10 5 keV clusters at z > 3 are expected in the Sloan Digital Sky Survey area. Too many such clusters can falsify the model; detection of clusters more massive than Coma at z > 1 violates ΛCDM at 95% confidence if their surface density exceeds 0.003 deg-2, or 120 on the whole sky.

We use cosmic microwave background data from WMAP, ACBAR, VSA and CBI, and galaxy power spectrum data from 2dF, to constrain flat cosmologies based on the Jordan–Brans–Dicke theory, using a Markov Chain Monte Carlo approach. Using a parametrization based on = 1/4!, and performing an exploration in the range ln 2 [−9, 3], we obtain a 95% marginalized probability bound of ln 120.

We use an array of high-resolution N-body simulations to determine the mass function of dark matter haloes at redshifts 10-30. We develop a new method for compensating for the effects of finite simulation volume that allows us to find an approximation to the true 'global' mass function. By simulating a wide range of volumes at different mass resolution, we calculate the abundance of haloes of mass 10 5-12 h -1 M ⊙ . This enables us to predict accurately the abundance of the haloes that host the sources that reionize the Universe. In particular, we focus on the small mass haloes (≥10 5.5-6 h -1 M ⊙ ) likely to harbour Population III stars where gas cools by molecular hydrogen emission, early galaxies in which baryons cool by atomic hydrogen emission at a virial temperature of ∼10 4 K (∼10 7.5-8 h -1 M ⊙ ), and massive galaxies that may be observable at redshift ∼10. When we combine our data with simulations that include high-mass haloes at low redshift, we find that the best fit to the halo mass function depends not only on the linear overdensity, as is commonly assumed in analytic models, but also on the slope of the linear power spectrum at the scale of the halo mass. The Press-Schechter model gives a poor fit to the halo mass function in the simulations at all epochs; the Sheth-Tormen model gives a better match, but still overpredicts the abundance of rare objects at all times by up to 50 per cent. Finally, we consider the consequences of the recently released WMAP 3-yr cosmological parameters. These lead to much less structure at high redshift, reducing the number of z = 10 'mini-haloes' by more than a factor of two and the number of z=30 galaxy hosts by nearly four orders of magnitude. Code to generate our best-fitting halo mass function may be downloaded from http://icc.dur.ac.uk/Research/PublicDownloads/genmf.readme.html.

We use a novel technique to simulate the growth of one of the most massive progenitors of a supercluster region from redshift z ∼ 80, when its mass was about 10 M ○. , until the present day. Our nested sequence of N-body resimulations allows us to study in detail the structure both of the dark matter object itself and of its environment. Our effective resolution is optimal at redshifts of 49, 29, 12, 5 and 0 when the dominant object has mass 1.2 x 10 5 ,5 × 10 7 ,2 × 10 10 , 3 x 10 12 and 8 × 10 14 h -1 M ○. , respectively, and contains ∼10 6 simulation particles within its virial radius. Extended Press-Schechter (EPS) theory correctly predicts both this rapid growth and the substantial overabundance of massive haloes we find at early times in regions surrounding the dominant object. Although the large-scale structure in these regions differs dramatically from a scaled version of its present-day counterpart, the internal structure of the dominant object is remarkably similar. Molecular hydrogen cooling could start as early as z ∼ 49 in this object, while cooling by atomic hydrogen becomes effective at z ∼ 39. If the first stars formed in haloes with virial temperature ∼ 2000 K, their comoving abundance at z = 49 should be similar to that of dwarf galaxies today, while their comoving correlation length should be ∼2.5 h -1 Mpc.

We use a high-accuracy computational code to investigate the precision with which cosmological parameters could be reconstructed by future cosmic microwave background experiments. We focus on the two planned satellite missions: MAP and Planck. We identify several parameter combinations that could be determined with a few percent accuracy with the two missions, as well as some degeneracies among the parameters that cannot be accurately resolved with the temperature data alone. These degeneracies can be broken by other astronomical measurements. Polarization measurements can significantly enhance the science return of both missions by allowing a more accurate determination of some cosmological parameters, by enabling the detection of gravity waves and by probing the ionization history of the universe. We also address the question of how Gaussian the likelihood function is around the maximum and whether gravitational lensing changes the constraints.

We use a combination of three large N-body simulations to investigate the dependence of dark matter halo concentrations on halo mass and redshift in the Wilkinson Microwave Anisotropy Probe year 5 (WMAP5) cosmology. The median relation between concentration and mass is adequately described by a power law for halo masses in the range 1011–1015 h−1 M⊙ and redshifts z < 2, regardless of whether the halo density profiles are fitted using Navarro, Frenk & White or Einasto profiles. Compared with recent analyses of the Millennium Simulation, which uses a value of σ8 that is higher than allowed by WMAP5, z= 0 halo concentrations are reduced by factors ranging from 23 per cent at 1011 h−1 M⊙ to 16 per cent at 1014 h−1 M⊙. The predicted concentrations are much lower than inferred from X-ray observations of groups and clusters.

We use Type Ia supernovae studied by the High-z Supernova Search Team to constrain the properties of an energy component that may have contributed to accelerating the cosmic expansion. We find that for a flat geometry the equation-of-state parameter for the unknown component, αx = Px/ρx, must be less than -0.55 (95% confidence) for any value of Ωm, and it is further limited to αx < -0.60 (95% confidence) if Ωm is assumed to be greater than 0.1. These values are inconsistent with the unknown component being topological defects such as domain walls, strings, or textures. The supernova (SN) data are consistent with a cosmological constant (αx = -1) or a scalar field that has had, on average, an equation-of-state parameter similar to the cosmological constant value of -1 over the redshift range of z ≈ 1 to the present. SN and cosmic microwave background observations give complementary constraints on the densities of matter and the unknown component. If only matter and vacuum energy are considered, then the current combined data sets provide direct evidence for a spatially flat universe with Ωtot = Ωm + ΩΛ = 0.94 ± 0.26 (1 σ).

We study the sample variance of the matter power spectrum for the standard Λ cold dark matter universe. We use a total of 5000 cosmological N-body simulations to study in detail the distribution of best-fit cosmological parameters and the baryon acoustic peak positions. The obtained distribution is compared with the results from the Fisher matrix analysis with and without including non-Gaussian errors. For the Fisher matrix analysis, we compute the derivatives of the matter power spectrum with respect to cosmological parameters using directly full nonlinear simulations. We show that the non-Gaussian errors increase the unmarginalized errors by up to a factor of five for kmax = 0.4 h Mpc−1 if there is only one free parameter, provided other parameters are well determined by external information. On the other hand, for multi-parameter fitting, the impact of the non-Gaussian errors is significantly mitigated due to severe parameter degeneracies in the power spectrum. The distribution of the acoustic peak positions is well described by a Gaussian distribution, with its width being consistent with the statistical interval predicted from the Fisher matrix. We also examine systematic bias in the best-fit parameter due to the non-Gaussian errors. The bias is found to be smaller than the 1σ statistical error for both the cosmological parameters and the acoustic scale positions.

We study the relation between the density distribution of tracers for large-scale struc- ture and the underlying matter distribution - commonly termed bias - in theCDM framework. In particular, we examine the validity of the local model of biasing at quadratic order in the matter density. This model is characterized by parameters b1 and b2. Using an ensemble of N-body simulations, we apply several statistical meth- ods to estimate the parameters. We measure halo and matter fluctuations smoothed on various scales. We find that, whilst the fits are reasonably good, the parameters vary with smoothing scale. We argue that, for real-space measurements, owing to the mixing of wavemodes, no smoothing scale can be found for which the parameters are independent of smoothing. However, this is not the case in Fourier space. We measure halo and halo-mass power spectra and from these construct estimates of the effective large-scale bias as a guide for b1. We measure the configuration dependence of the halo bispectra Bhhh and reduced bispectra Qhhh for very large-scale k-space triangles. From this data we constrain b1 and b2, taking into account the full bispectrum covariance matrix. Using the lowest-order perturbation theory, we find that for Bhhh the best-fit parameters are in reasonable agreement with one another as the triangle scale is var- ied; although, the fits become poor as smaller scales are included. The same is true for Qhhh. The best-fit values were found to depend on the discreteness correction. This led us to consider halo-mass cross-bispectra. The results from these statistics supported our earlier findings. We then developed a test to explore whether the inconsistency in the recovered bias parameters could be attributed to missing higher-order corrections in the models. We prove that low-order expansions are not sufficiently accurate to model the data, even on scales k1 � 0.04hMpc 1 . If robust inferences concerning bias are to be drawn from future galaxy surveys, then accurate models for the full nonlinear bispectrum and trispectrum will be essential.

We study the problem of separating E and B modes in interferometric observations of the polarization of the cosmic microwave background. The E and B band powers and their mixings are measured from both single-dish and interferometric mock observations using the quadratic estimator of maximum-likelihood analysis. We find that the interferometer can separate E and B modes in a single-pointing measurement and is thus well suited for detecting the faint-lensing-induced and gravity-wave-induced B modes. For mosaicking observations, compared to the single dish the interferometer is in general more efficient in separating E and B modes, and, for a high signal-to-noise ratio per pixel, it needs about 3 times fewer pixels to measure extremely blue polarization power spectra.

We study the physical limitations placed on cosmic microwave background (CMB) temperature and polarization measurements of the initial power spectrum. These limitations include geometric projection, acoustic physics, gravitational lensing and degeneracies with cosmological parameters. Detailed information on the spectrum is greatly assisted by polarization information and localized to the acoustic regime $k=0.02\ensuremath{-}0.2{\mathrm{Mpc}}^{\ensuremath{-}1}$ with a fundamental resolution of $\ensuremath{\Delta}k/kg0.05.$ From this study we construct principal component based statistics, which are orthogonal to cosmological parameters including the initial amplitude and tilt of the spectrum, that best probe deviations from scale-free initial conditions. These statistics resemble Fourier modes confined to the acoustic regime and ultimately can yield $\ensuremath{\sim}50$ independent measurements of the power spectrum features to percent level precision. They are straightforwardly related to more traditional parametrizations, such as the running of the tilt, and in the future can provide many statistically independent measurements of it for consistency checks. Though we mainly consider physical limitations on the measurements, these techniques can be readily adapted to include instrumental limitations or other sources of power spectrum information.

We study the large-scale anisotropic two-point correlation function using 46,760 luminous red galaxies at redshifts 0.16-0.47 from the Sloan Digital Sky Survey. We measure the correlation function as a function of separations parallel and perpendicular to the line of sight in order to take account of anisotropy of the large-scale structure in redshift space. We find a slight signal of baryonic features in the anisotropic correlation function, i.e., a “baryon ridge” corresponding to a baryon acoustic peak in the spherically averaged correlation function, which has already been reported using the same sample. The baryon ridge has primarily a spherical structure with a known radius in comoving coordinates. It enables us to divide the redshift distortion effects into dynamical and geometrical components and provides further constraints on cosmological parameters, including the dark energy equation-of-state. With an assumption of a flat Λ cosmology, we find the best-fit values of Ωm = 0.218−0.037+0.047 and Ωb = 0.047 ± 0.016 (68% CL) when we use the overall shape of the anisotropic correlation function of 40 < s < 200 h−1 Mpc including a scale of baryon acoustic oscillations. When an additional assumption of Ωbh2 = 0.024 is adopted, we obtain ΩDE = 0.770−0.040+0.051 and w = − 0.93−0.35+0.45. These constraints are estimated only from our data of the anisotropic correlation function, and they agree quite well with values both from the cosmic microwave background (CMB) anisotropies and from other complementary statistics using the LRG sample. With the CMB prior from the 3 year WMAP results, we give stronger constraints on those parameters.

We study the kinematics of the gaseous cosmic web at high redshift using Lyα forest absorption in multiple QSO sight lines. Observations of the projected velocity shifts between Lyα absorbers common to the lines of sight to a gravitationally lensed QSO and three more widely separated QSO pairs are used to directly measure the expansion of the cosmic web in units of the Hubble velocity, as a function of redshift and spatial scale. The lines of sight used span a redshift range from about 2 to 4.5 and represent transverse scales from the subkiloparsec range to about 300 h physical kpc. Using a simple analytic model and a cosmological hydrodynamic simulation, we constrain the underlying three-dimensional distribution of expansion velocities from the observed line-of-sight distribution of velocity shear across the plane of the sky. The shape of the shear distribution and its width (14.9 km s-1 rms for a physical transverse separation of 61 h kpc at z = 2, 30.0 km s-1 for 261 h kpc at z = 3.6) are found to be in good agreement with the IGM undergoing large-scale motions dominated by the Hubble flow, making this one of the most direct observations possible of the expansion of the universe. However, modeling the Lyα clouds with a simple "expanding pancake" model, the average expansion velocity of the gaseous structures causing the Lyα forest in the lower redshift (z ~ 2) smaller separation (61 kpc) sample appears about 20% lower than the local Hubble expansion velocity. In order to understand the observed velocity distribution further we investigated the statistical distribution of expansion velocities in cosmological Lyα forest simulations. The mean expansion velocity in the (z ~ 2, separation ~ 60 kpc) simulation is indeed somewhat smaller than the Hubble velocity, as found in the real data. We interpret this finding as tentative evidence for some Lyα forest clouds breaking away from the Hubble flow and undergoing the early stages of gravitational collapse. However, the distribution of velocities is highly skewed, and the majority of Lyα forest clouds at all redshifts from 2 to 3.8 expand with super-Hubble velocities, typically about 5%-20% faster than the Hubble flow. This behavior is explained if most Lyα forest clouds in the column density range typically detectable are expanding filaments that stretch and drain into more massive nodes. The significant difference seen in the velocity distributions between the high- and low-redshift samples may conceivably reflect actual peculiar deceleration, the differences in spatial scale, or our selecting higher densities at lower redshift for a given detection threshold for Lyα forest lines. We also investigate the alternative possibility that the velocity structure of the general Lyα forest could have an entirely different, local origin, as expected if the Lyα forest were produced or at least significantly modified by galactic feedback, e.g., winds from star-forming galaxies at high redshift. However, we find no evidence that the observed distribution of velocity shear is significantly influenced by processes other than Hubble expansion and gravitational instability. To avoid overly disturbing the IGM, galactic winds may be old and/or limp by the time we observe them in the Lyα forest, or they may occupy only an insignificant volume fraction of the IGM. We briefly discuss the observational evidence usually presented in favor of an IGM afflicted by high-redshift extragalactic superwinds and find much of it ambiguous. During the hierarchical buildup of structure, galaxies are expected to spill parts of their interstellar medium and to heat and stir the IGM in ways that make it hard to disentangle this gravitational process from the effects of winds.