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Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early Universe. We investigate how gravitational instability drives the distribution of these…
We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…
We investigate the evolution of the skewness of the distribution of density fluctuations in CDM models with both Gaussian and non--Gaussian initial fluctuations. We show that the method proposed by Coles \& Frenk (1991), which uses the…
Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters which govern them. The non-linear evolution of large scale structure produces a non-Gaussian signal which is…
We calculate the kurtosis of a large-scale density field which has undergone weakly non-linear gravitational evolution from arbitrary non-Gaussian initial conditions. It is well known that the weakly evolved {\twelveit skewness} is equal to…
Recent studies have demonstrated that {\em secondary} non-Gaussianity induced by gravity will be detected with a high signal-to-noise (S/N) by future and even by on-going weak lensing surveys. One way to characterise such non-Gaussianity is…
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational…
We compute the skewness $t_3$ and the corresponding hierarchical amplitude $T_3$ of the divergence of the velocity field for arbitrary non-Gaussian initial conditions. We find that $T_3$ qualitatively resembles the corresponding…
Bernardeau et al. (1997), using perturbation theory, showed that the skewness of the large-scale lensing-convergence, or projected mass density, could be used to constrain $\Omega_m$, the matter content of the universe. On the other hand,…
We computed the power spectrum of weak cosmic shear in models with non-Gaussian primordial density fluctuations. Cosmological initial conditions deviating from Gaussianity have recently attracted much attention in the literature, especially…
Is gravitational growth responsible for the observed large scale structure in the universe? Do we need non-gaussian initial conditions or non-gravitational physics to explain the large scale features traced by galaxy surveys? I will briefly…
This paper investigates whether nonlinear gravitational instability can account for the clustering of galaxies on large and small scales, and for the evolution of clustering with epoch. No CDM-like spectrum is consistent with the shape of…
The gravitational evolution of the genus of the density field in large-scale structure is analytically studied in a weakly nonlinear regime using second-order perturbation theory. Weakly nonlinear evolution produces asymmetry in the…
It is believed that the biasing of the galaxies plays an important role for understanding the large-scale structure of the universe. In general, the biasing of galaxy formation could be stochastic. Furthermore, the future galaxy survey…
We calculate the cosmological evolution of the 1-point probability distribution function (PDF), using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion of the PDF. Our method applies…
Continuous wavelet analysis has been increasingly employed in various fields of science and engineering due to its remarkable ability to maintain optimal resolution in both space and scale. Here, we introduce wavelet-based statistics,…
We explore the possibility of putting constraints on dark energy models with statistical property of large scale structure in the non-linear region. In particular, we investigate the $w$ dependence of non-Gaussianity of the smoothed density…
Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of…
The Universe is mostly composed of large and relatively empty domains known as cosmic voids, whereas its matter content is predominantly distributed along their boundaries. The remaining material inside them, either dark or luminous matter,…
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…