17 pages, 6 figures. Chapter of the volume ``Dynamics and Thermodynamics of systems with long range interactions: theory and experiments'', A. Campa, A. Giansanti, G. Morigi, F. Sylos Labini Eds., American Institute of Physics Conference proceedings, 970 (2008). See http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=970&Issue=1
We discuss the differences and analogies of gravitational clustering in finite and infinite systems. The process of collective, or violent, relaxation leading to the formation of quasi-stationary states is one of the distinguished features in the dynamics of self-gravitating systems. This occurs, in different conditions, both in a finite than in an infinite system, the latter embedded in a static or in an expanding background. We then discuss, by considering some simple and paradigmatic examples, the problems related to the definition of a mean-field approach to gravitational clustering, focusing on role of discrete fluctuations. The effect of these fluctuations is a basic issue to be clarified to establish the range of scales and times in which a collision-less approximation may describe the evolution of a self-gravitating system and for the theoretical modeling of the non-linear phase.
A brief summary of several topics in the study of gravitational many body problem is given. The discussion covers both static backgrounds (applicable to astrophysical systems) as well as clustering in an expanding background (relevant for cosmology)
A new approach to study the nonlinear phase of gravitational clustering in an expanding universe is explored. This approach is based on an integro-differential equation, for the evolution of the gravitational potential in the Fourier space, which is obtained by using a physically motivated closure condition. I show how this equation allows one to understand several aspects of nonlinear gravitational clustering and provides insight in to the transfer of power from one scale to another through nonlinear mode coupling.
Alignment of velocity and acceleration before shell crossing, and later misalignment are used to define velocity contrast, an indicator of dynamical state of matter undergoing gravitational collapse. We use this to study bias in clustering properties of dynamically nonlinear mass.
Several issues related to the gravitational clustering of collisionless dark matter in an expanding universe is discussed. The discussion is pedagogical but the emphasis is on semianalytic methods and open questions - rather than on well established results.
We study the CMB anisotropy induced by the non-linear perturbations in the massive neutrino density associated to the non-linear gravitational clustering proceses. Our results show that for the neutrino fraction in agreement with that indicated by the astroparticle and nuclear physics experiments and a cosmological accreting mass comparable with the mass of known clusters, the angular resolution and the sensitivity of the CMB anisotropy measurements from the Planck surveyor will allow the detection of the dynamical effects of the neutrino gravitational clustering.
We review current best estimates of the strength and detectability of the gravitational waves from a variety of sources, for both ground-based and space-based detectors, and we describe the information carried by the waves.
An analytical understanding of the strongly nonlinear regime of gravitational collapse has been difficult to achieve. The only insight has been the stable clustering hypothesis, which assumes that the number of neighbors for objects averaged over small length scales is constant in time. Our recently proposed analytic halo model for N-point correlation functions now provides a tool for calculating gravitational clustering properties in the strongly nonlinear regime. This model also provides a new physical framework for an independent evaluation of the validity of the stable clustering hypothesi…
We consider the problem of gravitational clustering in a D-dimensional expanding Universe and derive scaling relations connecting the exact mean two-point correlation function with the linear mean correlation function, in the quasi-linear and non-linear regimes, using the standard paradigms of scale-invariant radial collapse and stable clustering. We show that the existence of scaling laws is a generic feature of gravitational clustering in an expanding background, in all dimensions except D=2 and comment on the special nature of the 2-dimensional case. The D-dimensional scaling laws derived h…
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…
The interplay between gravitational and dispersive forces in a multi-streamed medium leads to an effect which is exposed in the present note as the genuine driving force of stabilization of large-scale structure. The conception of `adhesive gravitational clustering' is advanced to interlock the fairly well-understood epoch of formation of large-scale structure and the onset of virialization into objects that are dynamically in equilibrium with their large-scale structure environment. The classical `adhesion model' is opposed to a class of more general models traced from the physical origin of …
I review the theory of hierarchical clustering, starting with an historical overview and moving on to a discussion of those aspects of dissipationless clustering under gravity which are most relevant to galaxy formation. I conclude with some comments on the additional problems which arise when including all the other physics needed to build a realistic picture for the origin and evolution of the galaxy population.
I discuss new results concerning the evolution of the bispectrum due to gravitational instability from gaussian initial conditions using one-loop perturbation theory (PT). Particular attention is paid to the transition from weakly non-linear scales to the non-linear regime at small scales. Comparison with numerical simulations is made to assess the regime of validity of the perturbative approach.
The large-scale structure of the Universe is thought to evolve by a process of gravitational amplification from low-amplitude Gaussian noise generated in the early Universe. The later, non-linear stages of gravitation-induced clustering produce phase correlations with well-defined statistical properties. In particular, the distribution of phase differences $D$ between neighboring Fourier modes provides useful insights into the clustering phenomenon. Here we develop an approximate theory for the probability distribution $D$ and test it using a large battery of numerical simulations. We find a r…
We show that the predictions of the recent physical model by Granato et al. (2001) are fully consistent with the available estimates of the clustering properties of galaxies at (sub)-mm wavelengths. The model is then exploited to compute the expected power spectrum of fluctuations due to clustering at the frequencies of the High Frequency Instrument (HFI) of ESA's {\sc Planck} satellite. The clustering signal is found to be detectable in regions of low interstellar dust emission. A further distinctive prediction of the adopted model is a remarkably high fraction of gravitationally lensed sourc…
The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies investigated and solved up to the second order in earlier papers (Buchert 1992, Buchert \& Ehlers 1993) is evaluated up to the third order. On its basis a model for non-linear clustering applicable to the modeling of large-scale structure in the Universe for generic initial conditions is formulated. A truncated model is proposed which represents the ``main body'' of the perturbation sequence in the early non-linear regime by neglecting all gravitational sources which describe interaction of the perturbations. However, I also g…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in heirarchical models. This analysis leads to re…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime; (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in hierarchical models. This analysis leads to results …
A new method for analyzing point patterns produced by the evolution of gravitational clustering is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of anisotropic distributions. The statistical approach is based on the spherical harmonic expansion of angular correlations. A general introduction to the method is given; a theoretical analysis shows that it is partially connected with previous harmonic analyses applied to galaxy catalogs. The effectiveness of the statistical analysis in quantifying clustering mor…
I review several issues related to statistical description of gravitating systems in both static and expanding backgrounds. After briefly reviewing the results for the static background, I concentrate on gravitational clustering of collisionless particles in an expanding universe. In particular, I describe (a) how the non linear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale and (b) the asymptotic characteristics of gravitational clustering which are independent of the initial conditions. Numeri…
In the standard paradigm for cosmological structure formation, clustering develops from initially random-phase (Gaussian) density fluctuations in the early Universe by a process of gravitational instability. The later, non-linear stages of this process involve Fourier mode-mode interactions that result in a complex pattern of non-random phases. We present a novel mapping technique that reveals mode coupling induced by this form of nonlinear interaction and allows it to be quantified statistically. The phase mapping technique circumvents the difficulty of the circular characteristic of phi_k an…
The large-scale structure in the Universe is believed to arise out of small random density perturbations generated in the very early Universe, that are amplified by gravity. Large and usually intricate N-body simulations are typically employed to model the complex nonlinear dynamics in a self gravitating medium. We suggest a very simple model which predicts, on large scales, the correct density and velocity distributions. The model does not involve an explicit computation of the gravitational force. It is based on a simple transformation of the variables and local conservation laws of mass and…
We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $χ^2$ model, as motivated by some models of inflation. The emphasis is in signatures that can be used to constrain this type of models from large-scale structure galaxy surveys. Non-Gaussian initial conditions provide additional non-linear couplings otherwise forbidden by symmetry that cause non-linear gravitational corrections to become important at larger scales than in the Gaussian case. In fact, the lack of hierarchical scaling in the initial conditions is partially restored by gravitational evolut…
We study the non linear gravitational clustering of collisionless particles in an expanding background using an integro-differential equation for the gravitational potential. In particular, we address the question of how the nonlinear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale. We show that the dynamical equation allows self similar evolution for the gravitational potential $ϕ_{\bf k}(t)$ in Fourier space of the form $ϕ_{\bf k}(t) = F(t)D({\bf k}) $ where the function $F(t)$ satisfies a seco…
The scaling ansatz of Hamilton et al. effectively extends the idea of self-similar scaling to initial power spectra of any generic shape. Applications of this ansatz have provided a semi-empirical analytical description of gravitational clustering which is extremely useful. This contribution examines the two theoretical ingredients that form the basis of these applications: self-similar evolution and the stable clustering hypothesis. A brief summary of work verifying self-similar scaling for scale free spectra $P(k) \propto k^n$, with $n < -1$ is given. The main results presented here examine …
Two-body scattering and other discreteness effects are unimportant in cosmological gravitational clustering in most scenarios, since the dark matter has a small particle mass. The collective field should determine evolution: Two-body scattering in simulations violates the Poisson-Vlasov equations. We test this in PM, P$^3$M, Tree, and NGPM codes, noting that a collisionless code will preserve the one-dimensional character of plane wave collapse. We find collisionality vanishing as the softening parameter approaches the mean interparticle separation. Solutions for the problem are suggested, inv…
Weak gravitational lensing by large scale structure affects the number counts of faint galaxies through the ``magnification bias'' and thus affects the measurement of the angular two-point correlation function $\w $. At faint magnitudes the clustering amplitude will decrease differently with limiting magnitude than expected from Limber's equation. The amplitude will hit a minimum and then rise with limiting magnitude. This behavior occurs because $\w$ due to clustering decreases with distance, while the ``magnification bias'' due to weak lensing increases with distance. The apparent magnitude …
The power spectrum P(k)\propto k^n with n=-2 is close to the shape of the measured galaxy spectrum on small scales. Unfortunately this spectrum has proven rather difficult to simulate. Further, 2-dimensional simulations have suggested a breakdown of self-similar scaling for spectra with n<-1 due to divergent contributions from the coupling of long wave modes. This paper is the second (numerical) part of our investigation into the nonlinear gravitational clustering of scale-free spectra. Using high-resolution N-body simulations we find that the n=-2 power spectrum, as well as trajectories of th…
We show that the nonlinear evolution of the cosmic gravitational clustering is approximately spatial local in the $x$-$k$ (position-scale) phase space if the initial perturbations are Gaussian. That is, if viewing the mass field with modes in the phase space, the nonlinear evolution will cause strong coupling among modes with different scale $k$, but at the same spatial area $x$, while the modes at different area $x$ remain uncorrelated, or very weakly correlated. We first study the quasi-local clustering behavior with the halo model, and demonstrate that the quasi-local evolution in the phase…
The Press--Schechter description of gravitational clustering from an initially Poisson distribution is shown to be equivalent to the well studied Galton--Watson branching process. This correspondence is used to provide a detailed description of the evolution of hierarchical clustering, including a complete description of the merger history tree. The relation to branching process epidemic models means that the Press--Schechter description can also be understood using the formalism developed in the study of queues. The queueing theory formalism, also, is used to provide a complete description of…
Using an ensemble of high resolution 2D numerical simulations, we explore the scaling properties of cosmological density fluctuations in the non-linear regime. We study the scaling behaviour of the usual $N$--point volume-averaged correlations, and also examine the scaling of the entire probability density function (pdf) of the fluctuations. We focus on two important issues: (i) whether the scaling behaviour of 2D clustering is consistent with what one infer from radial collapse arguments; and (ii) whether there is any evidence from these high-resolution simulations that a regime of stable clu…
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 anti-correlated regions have important dynamical effects on {\it all} scales. In particular, the mere existence of negative values for the linear two-point correlation function $\xib_L$ over some range of scales starting from $l = L_o$, implies that the non-linear correlation function is bounded from above at {\it all} scales $x < L_o$. This also results in the relation $\xib \prop…
The theoretical basis for the prediction of anisotropies in the cosmic microwave background is very well developed. Very low amplitude density and temperature perturbations produce small gravitational effects, leading to an anisotropy that is a combination of temperature fluctuations at the surface of last scattering and gravitational redshifts both at last scattering and along the path to the observer. All of the primary anisotropy can be handled by linear perturbation theory, which allows a very accurate calculation of the predicted anisotropy from different models of the Universe.
We describe a new approach to gravitational instability in large-scale structure, where the equations of motion are written and solved as in field theory in terms of Feynman diagrams. The basic objects of interest are the propagator (which propagates solutions forward in time), the vertex (which describes non-linear interactions between waves) and a source with prescribed statistics which describes the effect of initial conditions. We show that loop corrections renormalize these quantities, and discuss applications of this formalism to a better understanding of gravitational instability and to…
We have studied the distribution of forces in gravitational systems through numerical experiments. Data were taken from an N-body simulation in an expanding universe. Before clustering, the distribution of random forces was represented as a Holtsmark distribution; the nearest-neighbor distribution is also shown as a comparison. The analytical and simulation distributions are in good agreement. When clustering becomes strong, the simulation result showed that the contribution of the forces acting on each galaxy, which is generated from all other galaxies, is almost entirely due to the gravitati…
We present the CMB anisotropy induced by the non-linear perturbations in the massive neutrino density associated to the non-linear gravitational clustering. We show that the non-linear time varying potential induced by the gravitational clustering process generates metric perturbations that affect the time evolution of the density fluctuations in all the components of the expanding Universe, leaving imprints on the CMB anisotropy power spectrum at subdegree angular scales. For a neutrino fraction in agreement with that indicated by the astroparticle and nuclear physics experiments and a cosmol…
The stable clustering hypothesis is a key analytical anchor on the nonlinear dynamics of gravitational clustering in cosmology. It states that on sufficiently small scales the mean pair velocity approaches zero, or equivalently, that the mean number of neighbours of a particle remains constant in time at a given physical separation. In this paper we use N-body simulations of scale free spectra P(k) \propto k^n with -2 \leq n \leq 0 and of the CDM spectrum to test for stable clustering using the time evolution and shape of the correlation function ξ(x,t), and the mean pair velocity on small sca…
Observations are compared to conflicting predictions about self-gravitational structure formation by the hydro-gravitational theory (HGT) of Gibson 1996-2003 versus cold-dark-matter hierarchical-clustering-cosmology (CDMHCC) and the Jeans 1902 criterion. According to HGT, gravitational structures form immediately after mass-energy equality by plasma fragmentation at 30,000 years when viscous and weak turbulence forces first balance gravitational forces within the horizon L_H = ct < L_J = c/[3ρG]^1/2, contrary to the Jeans 1902 criterion. Buoyancy forces fossilize the 10^-12 s^-1 rate-of-strain…
In an expanding universe, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality is unity and velocity and force field are equal. The Zeldovich approximation extends this feature beyond the linear regime, until formation of pancakes. Nonlinear clustering which takes place {\it after} the breakdown of Zeldovich approximation, breaks this relation and the mismatch between these two vectors increases as the evolution proceeds. We suggest th…
We discuss the late time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halo and the slope of the correlation function and discuss the conditions under which the slopes of the correlation function at the extreme nonl…
For a long time, gravitational instability in the disk of planetesimals has been suspected to be the main engine responsible for the beginning of dust growth, its advantage being that it provides for rapid growth. Its real importance in planetary formation is still debated, mainly because the potential presence of turbulence can prevent the settling of particles into a gravitationally unstable layer. However, several mechanisms could yield strongly inhomogeneous distributions of solids in the disk: radial drift, trapping in vortices, perturbations by other massive bodies, etc. In this paper we…
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight associated with any phase-space distribution function f(x,p,t). This action S describes both the average over the Gaussian initial conditions and the Vlasov-Poisson dynamics. Next, applying a standard method borrowed from field theory we generalize our problem to an N-field system and we look for an expansion over powers of 1/N. We describe three such methods and we…
We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. These methods can be classified into five types: (i) simple extrapolations from linear theory, such as the high--peak model and the lognormal model; (ii) {\em dynamical} approximations, including the Zel'dovich approximation and its extensions; (iii) non--linear models based on purely geometric considerations, of which the main example is the Voronoi model; (iv) statistical solutions involving scaling arguments, such as the hi…
The morphological nature of structures that form under gravitational instability has been of central interest to cosmology for over two decades. A remarkable feature of large scale structures in the Universe is that they occupy a relatively small fraction of the volume and yet show coherence on scales comparable to the survey size. With the aid of a useful synthesis of percolation analysis and shape statistics we explore the evolution of morphology of isolated density clumps in {\it real space} and that of the cluster distribution as a whole in scale-invariant cosmological models of gravitatio…
We study the nonlinear propagator, a key ingredient in renormalized perturbation theory (RPT) that allows a well-controlled extension of perturbation theory into the nonlinear regime. We show that it can be thought as measuring the memory of density and velocity fields to their initial conditions. This provides a clean definition of the validity of linear theory, which is shown to be much more restricted than usually recognized in the literature. We calculate the nonlinear propagator in RPT and compare to measurements in numerical simulations, showing remarkable agreement well into the nonline…
Hamilton et al. (1991) proposed a simple formula relating the nonlinear autocorrelation function of the mass distribution to the primordial spectrum of density fluctuations for gravitational clustering in an $Ω=1$ universe. High resolution N-body simulations show this formula to work well for scale-free spectra $P(k) \propto k^n$ when the spectral index $n\sim 0$, but not when $n \lsim -1$. We show that a modified version of the formula can work well provided its form depends on $n$. This dependence can be derived from a simple physical model for collapse from Gaussian initial conditions. Our …
We investigate the transfer of power between different scales and coupling of modes during non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales and use numerical simulations to study evolution of this power spectrum. Non-Linear effects generate power at other scales with most power flowing from larger to smaller scales. The ``cascade'' of power leads to equipartition of energy at smaller scales, implying a power spectrum with index $n\approx -1$. We find th…
The notion of `adhesion' has been advanced for the phenomenon of stabilization of large-scale structure emerging from gravitational instability of a cold medium. Recently, the physical origin of adhesion has been identified: a systematic derivation of the equations of motion for the density and the velocity fields leads naturally to the key equation of the `adhesion approximation' - however, under a set of strongly simplifying assumptions. In this work, we provide an evaluation of the current status of adhesive gravitational clustering and a clear explanation of the assumptions involved. Furth…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different fashion or involve different partial resummations. We focus on the two-point and three-point correlation functions, but these methods also apply to all higher-order correlation and response functions. We present the general formalism, which holds for the gravitational dynamics as well as for similar models, such as the Zeldovich dynamics, that obey similar …
In recent years there has been a developing realization that the interesting large--scale structure of voids, ``pancakes", and filaments in the Universe is a consequence of the efficacy of an approximation scheme for cosmological gravitation clustering proposal by Zel'dovich in 1970. However, this scheme was only supposed to apply to smoothed initial conditions, and its efficacy for hierarchical clustering has not been justified. We show that this is explained by the fact that the gravitationally evolved potential from N--body simulations closely resembles the smoothed potential of the initial…
We investigate the properties of the standard perturbative expansions which describe the early stages of the dynamics of gravitational clustering. We show that for hierarchical scenarios with no small-scale cutoff perturbation theory always breaks down beyond a finite order $q_+$. Besides, the degree of divergence increases with the order of the perturbative terms so that renormalization procedures cannot be applied. Nevertheless, we explain that despite the divergence of these subleading terms the results of perturbation theory are correct at leading order because they can be recovered throug…
This paper presents an analytical formula that closely approximates the fully nonlinear power spectrum of matter fluctuations for redshift $z\approx 5$ to 0 over a wide range of cosmologically interesting flat models with varying matter density $Ω_m$ and neutrino fraction $Ω_ν$. The functional form is motivated by analytical solutions in asymptotic regimes, but in order to obtain accurate approximations, the coefficients are calculated from fits to the nonlinear power spectrum computed from numerical simulations of four cosmological models. The transformation from the linear to nonlinear power…
I report on controlled comparison of gravitational approximation schemes linear/lognormal/adhesion/frozen-flow/Zel'dovich(ZA) and ZA's second--order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by finding an optimum smoothing window (see text) for the initial conditions. The Zel'dovich approximation, with optimized initial smoothing, worked extremely well. Its second-order generalization was slightly better. The success of our best-choice was a result of the treatment of the phases of nonlinear Fourier components. The adhesion app…
We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zel'dovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are Gaussian, the relation between the evolved DWT mode and the initial perturbations in the weakly non-linear regime is quasi-local. That is, the evolved density perturbations are mainly determined by the initial perturbations localized in the same spatial range. Furthermore, we show that the evolved mode is monotonically related to the initial perturbed mode. Thu…
We develop a simple analytic model for the gravitational clustering of dark haloes. The statistical properties of dark haloes are determined from the initial density field (assumed to be Gaussian) through an extension of the Press-Schechter formalism. Gravitational clustering is treated by a spherical model which describes the concentration of dark haloes in collapsing regions. We test this model against results from a variety of N-body simulations. The autocorrelation function of dark haloes in such simulations depends significantly on how haloes are identified. Our predictions agree well wit…
We quantitatively compare a particle implementation of the adhesion approximation to fully non--linear, numerical nbody simulations. Our primary tool, cross--correlation of nbody simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross--correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion a…
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit calculation of the second-order terms which are shown to agree with the results obtained from the hydrodynamical description of the system. Then, we explain that this identity extends to all orders of perturbation theory and that the perturbative series actually diverge for hierarchical scenarios. However, since the collisionless Boltzmann equation provides the exac…
Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational algorithm called SURFGEN which is used to determine the morphological and topological properties of the cosmic web. SURFGEN generates a triangulated surface from a discrete data set representing (say) the distribution of galaxies in real (or redshift) space. SURFGEN then determines, for this surface, the Minkowski functionals which provide us with an excellent d…
Padmanabhan (1996) has suggested a model to relate the nonlinear two - point correlation function to the linear two - point correlation function. In this paper, we extend this model in two directions: (1) By averaging over the initial Gaussian distribution of density contrasts, we estimate the spectral dependence of the scaling between nonlinear and linear correlation functions. (2) By using a physically motivated ansatz, we generalise the model to N-point correlation functions and relate the nonlinear, volume averaged, N-point correlation function $\barξ_N(x,a)$ with linearly extrapolated vol…
The weak lensing surveys have the potential to probe directly the clustering statistics of dark matter in the universe. Recent studies have shown that it is possible to predict analytically the whole probability distribution function (pdf) and the bias associated with the collapsed objects in the highly non-linear regime using the hierarchical ansatz. We extend such studies to the quasi-linear regime where the hierarchical ansatz is replaced by the tree-level perturbative calculations to an arbitrary order. It is shown how the generating function techniques can be coupled with the perturbative…
