We explore the possibility of improving the $Λ$CDM model at megaparsec scales by introducing a scalar interaction which increases the mutual gravitational attraction of dark matter particles. Using N-body simulations, we study the spatial distribution of dark matter particles and halos. We measure the effect of modifications in the Newton's gravity on properties of the two-point correlation function, the dark matter power spectrum, the cumulative halo mass function and density probability distribution functions. The results look promising: the scalar interactions produce desirable features at megaparsec scales without spoiling the $Λ$CDM successes at larger scales.
Using the Markov chain Monte Carlo (MCMC) method we perform a global analysis constraining the dynamics of dark energy in light of the supernova (Riess "Gold" samples), galaxy clustering (SDSS 3D power spectra and SDSS lyman-αforest information) and the latest three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations. We have allowed the dark energy equation of state to get across -1 and pay particular attention to the effects when incorrectly neglecting dark energy perturbations. We find the parameter space of dynamical dark energy is now well constrained and neglecting dark energy …
We highlight a viable mechanism leading to the formation of dark energy structures on sub-horizon cosmological scales, starting from linear perturbations in scalar-tensor cosmologies. We show that the coupling of the dark energy scalar field, or Quintessence, to the Ricci scalar induces a "dragging" of its density perturbations through the general relativistic gravitational potentials. We discuss, in particular, how this process forces dark energy to behave as a pressureless component if the cosmic evolution is dominated by non-relativistic matter. This property is also analyzed in terms of th…
A cosmological model with pressurelless matter and a fluid of negative pressure is studied. At perturbative level, fluctuations of both fluids are considered. It is shown that at least at very large scales, the fluid of negative pressure, which represents the dark energy content of the universe, clusters like the dust fluid. Numerical integration reveals that this behaviour may also occur at scales smaller than the Hubble radius.
Observing dark energy dynamics is the most important aspect of the dark energy research. In this paper we perform an analysis of the constraints on the property of dark energy from the current astronomical observations. We pay particular attention to the effects of dark energy perturbations. Using the data from SNIa (157 "gold" sample), WMAP and SDSS we find that the best fitting dark energy model is given by the dynamical model with the equation of state across -1. Nevertheless the standard \LambdaCDM models are still a very good fit to the current data and evidence for dynamics is currently …
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)
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…
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.
The influence of dark matter inhomogeneities on the angular size-redshift test is investigated for a large class of flat cosmological models driven by dark energy plus a cold dark matter component (XCDM model). The results are presented in two steps. First, the mass inhomogeneities are modeled by a generalized Zeldovich-Kantowski-Dyer-Roeder (ZKDR) distance which is characterized by a smoothness parameter $α(z)$ and a power index $γ$, and, second, we provide a statistical analysis to angular size data for a large sample of milliarcsecond compact radio sources. As a general result, we have foun…
Non-linear gravitational clustering in a universe dominated by dark energy, modelled by a `quintessence' scalar field, and cold dark matter with space-time varying mass is studied. Models of this type, where the variable mass is induced by dependence on the scalar field, as suggested by string theory or extra-dimensions, have been proposed as a viable solution of the coincidence problem. A general framework for the study of the non-linear phases of structure formation in scalar field cosmologies is provided, starting from a general relativistic treatment of the combined dark matter-dark energy…
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.
We provide a generic but physically clear discussion of the clustering properties of dark energy models. We explicitly show that in quintessence-type models the dark energy fluctuations, on scales smaller than the Hubble radius, are of the order of the perturbations to the Newtonian gravitational potential, hence necessarily small on cosmological scales. Moreover, comparable fluctuations are associated with different gauge choices. We also demonstrate that the often used homogeneous approximation is unrealistic, and that the so-called dark energy mutation is a trivial artifact of an effective,…
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.
The integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) as measured through its correlation with galaxies provides a unique opportunity to study the dynamics of the dark energy through its large scale clustering properties. Ultimately, a deep all-sky galaxy survey out to z~2 can make a 10sigma or ~10% measurement of the correlation and limit ~3% changes in the gravitational potential or total density fluctuation due to dark energy clustering on the Gpc scale. A canonical single scalar field or quintessence model predicts that these clustering effects will appear on the…
We derive the time evolution of the density contrast to all orders of perturbation theory, by solving the Einstein equation for scale-invariant fluctuations. These fluctuations are represented by an infinite series in inverse powers of the radial parameter. In addition to the standard growing modes, we find infinitely many more new growing modes for open and closed universes.
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.
Density profiles of cosmological virialized systems, or dark halos, have recently attracted much attention. I first present a brief historical review of numerical simulations to quantify the halo density profiles. Then I describe the latest results on the universal density profile and their observational confrontation. Finally I discuss a clustering model of those halos with particular emphasis on the cosmological light-cone effect.
(abridged) A wide-field galaxy redshift survey allows one to probe galaxy clustering at largest spatial scales, which carries an invaluable information on horizon-scale physics complementarily to the cosmic microwave background (CMB). Assuming the planned survey consisting of z~1 and z~3 surveys with areas of 2000 and 300 square degrees, respectively, we study the prospects for probing dark energy clustering from the measured galaxy power spectrum, assuming the dynamical properties of dark energy are specified in terms of the equation of state and the effective sound speed c_e in the context o…
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…
The problem of explaining the acceleration of the expansion of the universe and the observational and theoretical difficulties associated with dark matter and dark energy are discussed. The possibility that Einstein gravity does not correctly describe the large-scale structure of the universe is considered and an alternative gravity theory is proposed as a possible resolution to the problems.
Two methods of constraining the properties of dark energy are weak lensing tomography and cluster counting. Uncertainties in mass calibration of clusters can be reduced by using the properties of halo clustering (the clustering of clusters). However, within a single survey, weak lensing and halo clustering probe the same density fluctuations. We explore the question of whether this information can be used twice -- once in weak lensing and then again in halo clustering to calibrate cluster masses -- or whether the combined dark energy constraints are weaker than the sum of the individual constr…
We study the gravitational clustering of big bang relic neutrinos onto existing cold dark matter (CDM) and baryonic structures within the flat $Λ$CDM model, using both numerical simulations and a semi-analytical linear technique, with the aim of understanding the neutrinos' clustering properties for direct detection purposes. In a comparative analysis, we find that the linear technique systematically underestimates the amount of clustering for a wide range of CDM halo and neutrino masses. This invalidates earlier claims of the technique's applicability. We then compute the exact phase space di…
The potential is a constant to linear order in cosmological gravitational clustering. In this Letter we present results of testing the conjecture, proposed by Pauls and Melott (1995), that the effect of nonlinear evolution on the potential can be better described by smoothing it on the scale of nonlinearity. We show two-dimensional simulations consisting of an N-body code in which particles are accelerated not by their mutual attraction, but by the gradient of the initial potential smoothed on the current scale of nonlinearity. This approximation produces results considerably improved over usi…
We show the apparent redshift-space clustering of galaxies in redshift range of 0.2--0.4 provides surprisingly useful constraints on dark energy component in the universe, because of the right balance between the density of objects and the survey depth. We apply Fisher matrix analysis to the the Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS), as a concrete example. Possible degeneracies in the evolution of the equation of state (EOS) and the other cosmological parameters are clarified.
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…
Using the spectacular new high redshift supernova observations from the HST/GOODS program and previous supernova, CMB and galaxy clustering data, we make the most accurate measurements to date of the dark energy density rho_X as a function of cosmic time, constraining it in a rather model-independent way, assuming a flat universe. We find that Einstein's vanilla scenario where rho_X(z) is constant remains consistent with these new tight constraints, and that a Big Crunch or Big Rip is more than 50 gigayears away for a broader class of models allowing such cataclysmic events. We discuss popular…
We critically examine the reliability of the dark matter clustering in high-resolution cosmological $N$-body simulations on scales below the mean separation length of particles. The particle discreteness effect imposes the two fundamental limitations on those scales; the lack of the initial fluctuation power and the finite mass resolution. We address this problem applying the dark halo approach and are able to discuss separately how those two limitations affect the dark matter clustering in $N$-body simulations at early epochs. We find that limitations of the dark matter clustering are primari…
There has been some recent activity in trying to understand the dark matter clustering properties in the quasilinear regime, through resummation of perturbative terms, otherwise known as the renormalized perturbation theory (astro-ph/0509418), or the renormalization group method (astro-ph/0606028). While it is not always clear why such methods should work so well, there is no reason for them to capture non-perturbative events such as shell-crossing. In order to estimate the magnitude of non-perturbative effects, we introduce a (hypothetical) model of sticky dark matter, which only differs from…
This article addresses some issues related to statistical description of gravitating systems in an expanding backgrounds. 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) what are the asymptotic characteristics of gravitational clustering that are independent of the initial conditions. The analysis uses a new approach based on an integro-differential equation for the evolution of the gravitational potential in the Fourier space. I show how t…
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 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…
We study the evolution of galaxy clustering in various cosmological models with quintessence. We investigate how the analytical predictions vary with change of dark energy equation of state $w_X$. Comparing these predictions against available data we discuss to what extent the problems of galaxy biasing can be modelled. This will be key in constraining the dark energy equation of state with future galaxy surveys. We use a compilation of various surveys to study the number density and amplitude of galaxy clustering from observations of the local universe at $z \sim 0$ to that of the Lyman break…
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 …
We discuss some recent progress in constructing analytic approximations to the galaxy clustering. We show that successful models can be constructed for the clustering of both dark matter and dark matter haloes. Our understanding of galaxy clustering and galaxy biasing can be greatly enhanced by these models.
Redshift distortions, both geometrical and kinematical, of quasar clustering are simulated, for the Two-Degree Field QSO Redshift Survey (2QZ), showing that they are very effective to constrain the cosmological density and equation of state parameters, Omega_{m0}, Omega_{x0} and w. Particularly, it emerges that, for the cosmological constant case, the test is especially sensitive to the difference Omega_{m0} - Omega_{Lambda 0}, whereas, for the spatially flat case, it is quite competitive with future supernova and galaxy count tests, besides being complimentary to them.
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…
In this paper we study the angular momentum properties of simulated dark matter halos at high redshift that likely host the first stars in the Universe. Calculating the spin distributions of these $10^6 - 10^7 \Msun$ halos in redshift slices from $z = 15 - 6$, we find that they are well fit by a log-normal distribution as is found for lower redshift and more massive halos in earlier work. We find that both the mean value of the spin and dispersion are largely unchanged with redshift for all halos. Our key result is that subsamples of low and high spin $10^6 \Msun$ and $10^7 \Msun$ halos show d…
We investigate the structure of the dark matter halo formed in three different cold dark matter scenarios. We performed N-body simulations of formation of 13 cluster-sized halos. In all runs, density cusps proportional to $r^{-1.5}$ developed at the center. This result was independent of the cosmological models we simulated. We could not reproduce the cusp shallower than $r^{-1.5}$, which was obtained in some of previous studies. We also found that in all runs the density structure evolves in a self-similar way, even in $Ω\ne 1$ universes. These results show that the formation of structural fo…
A phenomenological model for the clustering of dark matter halos on the light-cone is presented. In particular, an empirical prescription for the scale-, mass-, and time-dependence of halo biasing is described in detail. A comparison of the model predictions against the light-cone output from the Hubble Volume $N$-body simulation indicates that the present model is fairly accurate for scale above $\sim 5h^{-1}$Mpc. Then I argue that the practical limitation in applying this model comes from the fact that we have not yet fully understood what are clusters of galaxies, especially at high redshif…
We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the `excursion set' approach by Bond et al., which automatically accounts for the `cloud-in-cloud' problem in the identification of bound systems. Our method allows to calculate correlation functions of haloes in Lagrangian space using either a multi-dimensional Fokker-Planck equation with suitable boundary conditions or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical …
We develop a phenomenological model to predict the clustering of dark matter halos on the light-cone by combining several existing theoretical models. Assuming that the velocity field of halos on large scales is approximated by linear theory, we propose an empirical prescription of a scale-, mass-, and time-dependence of halo biasing. We test our model against the Hubble Volume $N$-body simulation and examine its validity and limitations. We find a good agreement in two-point correlation functions of dark matter halos between the phenomenological model predictions and measurements from the sim…
We investigate the clustering properties of high-redshift galaxies within three competing scenarios for assigning luminous galaxies to dark matter halos from N-body simulations: a one galaxy per massive halo model, a quiescent star formation model, and a collisional starburst model. We compare these models to observations of Lyman-Break galaxies at z~3$ With current data and the simple statistic used here, one cannot rule out any of these models, but we see potential for finding distinguishing features using statistics that are sensitive to the tails of the distribution, and statistics based o…
We study the clustering properties of galaxy clusters expected to be observed by various forthcoming surveys both in the X-ray and sub-mm regimes by the thermal Sunyaev-Zel'dovich effect. Several different background cosmological models are assumed, including the concordance $Λ$CDM and various cosmologies with dynamical evolution of the dark energy. Particular attention is paid to models with a significant contribution of dark energy at early times which affects the process of structure formation. Past light cone and selection effects in cluster catalogs are carefully modeled by realistic scal…
The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, $ζ$, obeys the scaling law $ζ\propto ξ^{\frac{3m+4w-2ε}{2m+2w}}$ in the nonlinear regime, where $ξ$, $m$, $w$, and $ε$ are the two-point correlation function, the power index of the power spectrum in the nonlinear regime, the number of spatial dimensions, and the power index of the phase correlations, respectively. The new formula reveals the origin of the power index of the th…
In this paper we study the clustering of SZ-selected galaxy clusters on a past light-cone, particularly paying attention to the possibility of constraining properties of dark energy. The prospects of detecting baryonic features in the cluster power spectrum for a wide and shallow survey like PLANCK, and for an SPT-like narrow and deep survey are discussed. It is demonstrated that these future blank sky SZ surveys will have capability to improve significantly over the recently announced detection of baryonic oscillations based on the SDSS Luminous Red Galaxy (LRG) sample. We carry out parameter…
We investigate the clustering of high redshift galaxies in five variants of the cold dark matter (CDM) scenario, using hydrodynamic cosmological simulations that resolve the formation of systems with circular velocities $v_c \geq 100 \kms$ ($Ω=1$) or $v_c \geq 70 \kms$ ($Ω=0.4$). Although the five models differ in their cosmological parameters and in the shapes and amplitudes of their mass power spectra, they predict remarkably similar galaxy clustering at $z=2$, 3, and 4. The galaxy correlation functions show almost no evolution over this redshift range, even though the mass correlation funct…
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…
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…
We investigate the structure of the dark matter halo formed in the cold dark matter scenarios by N-body simulations with parallel treecode on GRAPE cluster systems. We simulated 8 halos with the mass of $4.4\times 10^{14}M_{\odot}$ to $1.6\times 10^{15}M_{\odot}$ in the SCDM and LCDM model using up to 30 million particles. With the resolution of our simulations, the density profile is reliable down to 0.2 percent of the virial radius. Our results show that the slope of inner cusp within 1 percent virial radius is shallower than -1.5, and the radius where the shallowing starts exhibits run-to-r…
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 investigate an analytic model to compute nonlinear power spectrum of dark matter, galaxies and their cross-correlation. The model is based on Press-Schechter halos, which cluster and have realistic dark matter profiles. The total power spectrum is a sum of two contributions, one from correlations betwen the halos and one from correlations within the same halo. We show that such a model can give dark matter power spectra which match well with the results of N-body simulations, provided that concentration parameter decreases with the halo mass. Galaxy power spectrum differs from dark matter p…
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, focus…
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 …
