The importance of Fourier phases for the morphology of gravitational clustering

The phases of the Fourier modes appearing in a plane-wave expansion of cosmological density fields play a vital role in determining the morphology of gravitationally developed clustering. We demonstrate this qualitatively and quantitatively using simulations. In particular, we use cross-correlation and rank-correlation techniques to quantify the agreement between a simulated distribution and phase-only reconstructions. The phase-only reconstructions exhibit a high degree of correlation with the original distributions, showing how meaningful spatial reconstruction of cosmological density fields depends more on phase accuracy than on amplitudes.     

The effects of anticorrelation on gravitational clustering

We use non-linear scaling relations (NSRs) to investigate the effects arising from the existence of negative correlations on the evolution of gravitational clustering in an expanding universe. It turns out that such anticorrelated regions have important dynamical effects on all scales. In particular, the mere existence of negative values for the linear two-point correlation function ξ¯ _L over some range of scales starting from l = L ₀ implies that the non-linear correlation function is bounded from above at all scales x < L ₀ . This also results in the relation ξ¯   ∝  x ⁻³ , at these scales, at late times, independent of the original form of the correlation function. Current observations do not rule out the existence of negative ξ¯ for 200  h ⁻¹ Mpc≲ ξ¯ ≲1000  h ⁻¹ Mpc; the present work may thus have relevance for the real Universe. The only assumption made in the analysis is the existence of NSR; the results are independent of the form of the NSR as well as of the stable clustering hypothesis.     

Generalized cumulant correlators and hierarchical clustering

The cumulant correlators, C _pq , are statistical quantities that generalize the better-known S _p parameters; the former are obtained from the two-point probability distribution function of the density fluctuations while the latter describe only the one-point distribution. If galaxy clustering develops from Gaussian initial fluctuations and a small-angle approximation is adopted, standard perturbative methods suggest a particular hierarchical relationship of the C _pq for projected clustering data, such as that obtained from the Automatic Plate Measuring (APM) survey. We establish the usefulness of the two-point cumulants for describing hierarchical clustering by comparing such calculations against available measurements from projected catalogues, finding very good agreement. We extend the idea of cumulant correlators to multipoint generalized cumulant correlators (related to the higher-order correlation functions). We extend previous studies in the highly non-linear regime to express the generalized cumulant correlators in terms of the underlying 'tree amplitudes' of hierarchical scaling models. Such considerations lead to a technique for determining these hierarchical amplitudes, to arbitrary order, from galaxy catalogues and numerical simulations. Knowledge of these amplitudes yields important clues about the phenomenology of gravitational clustering. For instance, we show that a three-point cumulant correlator can be used to separate the tree amplitudes up to sixth order. We also combine the particular hierarchical Ansatz of Bernardeau & Schaeffer with extended and hyper-extended perturbation theory to infer values of the tree amplitudes in the highly non-linear regime.     

Weak lensing from strong clustering

We investigate the effect of weak gravitational lensing in the limit of small angular scales where projected galaxy clustering is strongly non-linear. This is the regime likely to be probed by future weak lensing surveys. We use well-motivated hierarchical scaling arguments and the plane-parallel approximation to study multi-point statistical properties of the convergence field. These statistics can be used to compute the vertex amplitudes in tree models of hierarchical clustering; these can be compared with similar measurements from galaxy surveys, leading to a powerful probe of galaxy bias.     

Secondary gravitational anisotropies in open universes

The applicability of the potential approximation in the case of open universes is tested. Great Attractor-like structures are considered in the test. Previous estimates of the cosmic microwave background anisotropies produced by these structures are analysed and interpreted. The anisotropies corresponding to inhomogeneous ellipsoidal models are also computed. It is proved that, whatever the spatial symmetry may be, Great Attractor-like objects with extended cores (radii ∼10 h ⁻¹), located at redshift z =5.9 in an open universe with density parameter Ω₀=0.2, produce secondary gravitational anisotropies of the order of 10⁻⁵ on angular scales of a few degrees. The amplitudes and angular scales of the estimated anisotropy decrease as the Great Attractor size decreases. For comparable normalizations and compensations, the anisotropy produced by spherical realizations is found to be smaller than that of ellipsoidal models. This anisotropy appears to be an integrated effect along the photon geodesics. Its angular scale is much greater than that subtended by the Great Attractor itself. This is easily understood by taking into account the fact that the integrated effect is produced by the variations of the gravitational potential, which seem to be important in large regions subtending angular scales of several degrees. As a result of the large size of these regions, the spatial curvature of the universe becomes important and, consequently, significant errors (∼30 per cent) arise in estimates based on the potential approximation. As is emphasized in this paper, two facts should be taken into account carefully in some numerical estimates of secondary gravitational anisotropies in open universes: (1) the importance of scales much greater than those subtended by the cosmological structures themselves, and (2) the compatibility of the potential approximation with the largest scales.     

Evolution of galaxy clustering

We study the evolution of the correlation function of dark matter haloes in the CDM class of models. We show that the halo correlation function does not evolve in proportion with the correlation function of the underlying mass distribution. The earliest haloes to collapse, which correspond to rare peaks in the density field, cluster very strongly. The amplitude of the halo correlation function decreases from its initial, large, value. This decrease continues until the average peaks have collapsed, after which the amplitude grows slowly. This behaviour is shown to be generic and the epoch of minimum amplitude depends only on the rms  fluctuations in mass at the relevant scale and, to a much smaller extent, on the slope of the power spectrum at that scale. We discuss the relevance of this result for interpretation of observations of galaxy and quasar clustering.     

A two-dimensional analysis of percolation and filamentarity in the Sloan Digital Sky Survey Data Release One

We have used the largest cluster statistics and the average filamentarity to quantify respectively the connectivity and the shapes of the patterns seen in the galaxy distribution in two volume-limited subsamples extracted from the equatorial strips of the Sloan Digital Sky Survey (SDSS) Data Release One (DR1). The data was projected on to the equatorial plane and analysed in two dimensions (2D). Comparing the results with Poisson point distributions at various levels of smoothing we find evidence for a network-like topology with filaments being the dominant patterns in the galaxy distribution. With increasing smoothing, a transition from many individual filamentary structures to an interconnected network is found to occur at a filling factor of 0.5–0.6. We have tested the possibility that the connectivity and the morphology of the patterns in the galaxy distribution may be luminosity dependent and find significant evidence for a luminosity–morphology relation, the brighter galaxies exhibiting lower levels of connectivity and filamentarity compared to the fainter ones. Using a statistical technique, Shuffle, we show that the filamentarity in both the SDSS strips is statistically significant up to 80  h ⁻¹ Mpc but not beyond. Larger filaments, though identified, are not statistically significant. Our findings reaffirm earlier work establishing the filaments to be the largest known statistically significant coherent structures in the Universe.     

Cosmic statistics through weak lenses

Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical ansatz, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small angular scales (i.e. at high resolution), where the usual perturbative calculations of matter clustering no longer apply. We build on these studies in order to develop a complete picture of weak lensing at small smoothing angles. In particular, we study the full probability distribution function, bias and other multipoint statistics for the 'hot spots' of the convergence field induced by weak lensing, and relate these to the statistics of overdense regions in the underlying mass distribution. It is already known that weak lensing can constrain the background geometry of the Universe, but we further show that it can also provide valuable information about the statistics of collapsed objects and the physics of collisionless clustering. Our results are particularly important for future observations which will, at least initially, focus on small smoothing angles.     

Global textures and the formation of self-bound gravitational systems

Using a Newtonian approximation we developed a quantitative criterion for the collapse of a spherical distribution of matter under an isolated texture field. In particular, we found the evolution of an overdense region is strongly determined by two parameters: the energy scale of symmetry breaking ( η ) and the initial radius of the system. Applying our collapse criterion to typical galaxy scales we verified the formation of 10¹¹‐M_⊙ objects at z ≲9 and 10¹²‐M_⊙ objects at z ≲5.