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We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
The bispectrum, the three-point function of density fluctuations in Fourier space, is the lowest order statistic that carries information about the spatial coherence of large-scale structures. For Gaussian initial conditions, when the…
We investigate the non-gaussian properties of cosmic-string-seeded linear density perturbations with cold and hot dark matter backgrounds, using high-resolution numerical simulations. We compute the one-point probability density function of…
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…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
The power spectrum is widely used in astronomy, to analyze temporal or spatial structure. In cosmology, it is used to quantify large-scale structure (LSS) and the cosmic microwave background (CMB). This is because the power spectrum…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
We present and test a framework that models the three-dimensional distribution of mass in the Universe as a function of cosmological and astrophysical parameters. Our approach combines two different techniques: a rescaling algorithm that…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
In this work we investigate the generation of mock halo catalogues based on perturbation theory and nonlinear stochastic biasing with the novel PATCHY-code. In particular, we use Augmented Lagrangian Perturbation Theory (ALPT) to generate a…
We present a fully probabilistic, physical model of the non-linearly evolved density field, as probed by realistic galaxy surveys. Our model is valid in the linear and mildly non-linear regimes and uses second order Lagrangian perturbation…
This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in…
We calculate the higher order moments in a sequence of models where the initial density fluctuations are drawn from a chi^2_nu distribution with a power-law power spectrum. For large values of nu the distribution is approximately gaussian,…
Applying a transformation to a non-Gaussian field can enhance the information content of the resulting power spectrum, by reducing the correlations between Fourier modes. In the context of weak gravitational lensing, it has been shown that…
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum…
Recently Eisenstein and collaborators introduced a method to `reconstruct' the linear power spectrum from a non-linearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We…