Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure

Gravitational clustering in the nonlinear regime remains poorly understood. Gravity dual of gravitational clustering has recently been proposed as a means to study the nonlinear regime. The stable clustering ansatz remains a key ingredient to our understanding of gravitational clustering in the highly nonlinear regime. We study certain aspects of violation of the stable clustering ansatz in the gravity dual of Large Scale Structure (LSS). We extend the recent studies of gravitational clustering using AdS gravity dual to take into account possible departure from the stable clustering ansatz and to arbitrary dimensions. Next, we extend the recently introduced consistency relations to arbitrary dimensions. We use the consistency relations to test the commonly used models of gravitational clustering including the halo models and hierarchical ans\"atze. In particular we establish a tower of consistency relations for the hierarchical amplitudes: $Q, R_a, R_b, S_a,S_b,S_c$ etc. as a functions of the scaled peculiar velocity $h$. We also study the variants of popular halo models in this context. In contrast to recent claims, none of these models, in their simplest incarnation, seem to satisfy the consistency relations in the soft limit.Comment: 21 pages, 4 figure

Turbulence models of gravitational clustering

Large-scale structure formation can be modeled as a nonlinear process that transfers energy from the largest scales to successively smaller scales until it is dissipated, in analogy with Kolmogorov's cascade model of incompressible turbulence. However, cosmic turbulence is very compressible, and vorticity plays a secondary role in it. The simplest model of cosmic turbulence is the adhesion model, which can be studied perturbatively or adapting to it Kolmogorov's non-perturbative approach to incompressible turbulence. This approach leads to observationally testable predictions, e.g., to the power-law exponent of the matter density two-point correlation function.Comment: 5 pages; contribution to Spanish Relativity Meeting 2011; based on arXiv:1202.3011, with a brief discussion of relativistic aspect

An Indicator of Nonlinear Gravitational Clustering

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.Comment: 4 pages, uuencoded postscript file. To appear in 'Clusters, Lensing, and the Future of the Universe' ed. V.Trimble and A.Reisenegge

Non-Gaussian gravitational clustering field statistics

In this work we investigate the multivariate statistical description of the matter distribution in the nonlinear regime. We introduce the multivariate Edgeworth expansion of the lognormal distribution to model the cosmological matter field. Such a technique could be useful to generate and reconstruct three-dimensional nonlinear cosmological density fields with the information of higher order correlation functions. We explicitly calculate the expansion up to third order in perturbation theory making use of the multivariate Hermite polynomials up to sixth order. The probability distribution function for the matter field includes at this level the two-point, the three-point and the four-point correlation functions. We use the hierarchical model to formulate the higher order correlation functions based on combinations of the two-point correlation function. This permits us to find compact expressions for the skewness and kurtosis terms of the expanded lognormal field which can be efficiently computed. The method is, however, flexible to incorporate arbitrary higher order correlation functions which have analytical expressions. The applications of such a technique can be especially useful to perform weak-lensing or neutral hydrogen 21 cm line tomography, as well as to directly use the galaxy distribution or the Lyman-alpha forest to study structure formation.Comment: 20 pages, 2 figures; accepted in MNRAS 2011 August 22, in original form 2010 December 14 published, Publication Date: 03/201

Gravitational clustering in N-body simulations

In this talk we discuss some of the main theoretical problems in the understanding of the statistical properties of gravity. By means of N-body simulations we approach the problem of understanding the r\^ole of gravity in the clustering of a finite set of N-interacting particles which samples a portion of an infinite system. Through the use of the conditional average density, we study the evolution of the clustering for the system putting in evidence some interesting and not yet understood features of the process.Comment: 5 pages, 1 figur

Gravitational Clustering from Chi^2 Initial Conditions

We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $\chi^2$ 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 evolution at scales $k> 0.1$ h/Mpc. However, the bispectrum shows much larger amplitude and residual scale dependence not present in evolution from Gaussian initial conditions that can be used to test this model against observations. We include the effects of biasing and redshift distortions essential to compare this model with galaxy redshift surveys. We also discuss the effects of primordial non-Gaussianity on the redshift-space power spectrum and show that it changes the shape of the quadrupole to monopole ratio through non-linear corrections to infall velocities.Comment: 20 pages, 7 figure

Nonlinear Gravitational Clustering: dreams of a paradigm

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 nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile which preserves the shape at late times, then the correlation function should grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. We prove that such exact solutions do not exist; however, ther e exists a class of solutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$ to a good approximation. It turns out that the PLP's are the correlation functions which arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implicatios of this result.Comment: 32 Pages, Submitted to Ap