Related papers: Cosmology in One Dimension: Fractal Geometry, Powe…
We examine the fractal structure of the physical universe from the large scale to the smallest scale, including the phenomenon of fractal scaling. This is explained in terms of a stochastic underpinning for the laws of physics. A picture in…
Catalogues of galaxies, clusters of galaxies and superclusters - sources of information to study the large-scale structure of the Universe are reviewed. The power spectrum of density perturbations, and the correlation function are discussed…
This comment is in response to the paper by L. Guzzo recently appeared in ``New Astronomy'' related to our work. The subject of the discussion concerns the correlation properties of galaxy distribution in the available 3-d samples. There is…
How is the universe organized on large scales? How did this structure evolve from the unknown initial conditions to the present time? The answers to these questions will shed light on the cosmology we live in, the amount, composition and…
In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and…
We study here, from first principles, what properties of voids are to be expected in a fractal point distribution and how the void distribution is related to its morphology. We show this relation in various examples and apply our results to…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
The isothermal dynamical evolution of a clumpy and turbulent molecular cloud region and its fragmentation into a protostellar cluster is investigated numerically. The effect of different initial density and velocity distributions, generated…
This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous,…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Their ubiquity and extreme densities make star clusters probes of prime importance of galaxy evolution. Old globular clusters keep imprints of the physical conditions of their assembly in the early Universe, and younger stellar objects,…
There is evidence of a scale-invariant matter distribution up to scales over 10 Megaparsecs. We review scaling (fractal or multifractal) models of large scale structure and their observational evidence. We conclude that the dynamics of…
We present an analysis of the clustering evolution of dark matter in four cold dark matter (CDM) cosmologies. We use a suite of high resolution, 17-million particle, N-body simulations which sample volumes large enough to give clustering…
I review the standard paradigm for understanding the formation and evolution of cosmic structure, based on the gravitational instability of dark matter, but many variations on this basic theme are viable. Despite the great progress that has…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
Unless there is evidence for fractal scaling with a single exponent over distances .1 <= r <= 100 h^-1 Mpc then the widely accepted notion of scale invariance of the correlation integral for .1 <= r <= 10 h^-1 Mpc must be questioned. The…
In the standard picture of cosmological structure formation, the Universe we see today is evolved under the gravitational instability from tiny random fluctuations. In this talk I discuss the onset of non-linearity in the large scale…
Recently, the observed cellular nature of the large-scale structure of the Universe with its quasi-regular pattern of superclusters and voids has been pointed out by several authors. In this paper, we investigate properties of the initial…
We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale…