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Cosmology in one dimension: multifractal analysis of hierarchical clustering
Shiozawa, Yui
Shiozawa, Yui
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2016
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Abstract
While the universe we observe today exhibits local filament-like structures, with stellar clusters and large voids between them, the primordial universe is believed to have been nearly homogeneous with slight variations in matter density. To understand how the observed hierarchical structure was formed, researchers have developed a one-dimensional analogue of the universe that can simulate the evolution of a large number of matter particles. Investigations to date demonstrate that this model reveals structure formation that shares essential features with the three-dimensional observations. In the present work, we have expanded on this concept to include two species of matter, specifically dark matter and luminous matter. In our simulation, luminous matter is treated in a way that loses energy in interaction. The results of the simulations clearly show the formation of a Cantor set like multifractal pattern over time.^In contrast with most earlier studies, mass-oriented methods for computing multifractal dimensions were applied to analyze the bottom-up structure formation. We found that the multifractal spectra for two types of matter differ in the dense regions. This confirms that the luminous matter distribution does not equally trace the dark matter distribution. In order to understand the dynamics of hierarchical clustering process, we investigate three different cluster definitions and examine the clusters defined by each algorithm. In general, a given cluster does not remain isolated long enough before it merges with neighboring clusters. Therefore clusters are not completely virialized and substructure within the clusters persists over time. As the existence of substructure is a hallmark of fractal geometry, we argue that clusters in the model are best characterized by multifractal measures instead of smoothed theoretical functions.^This implies that the statistics obtained from the distribution of clusters and within them may not satisfactorily impose constraints on cosmological parameters and the nature of dark matter as often assumed.
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Subject
Subject(s)
Fractals.
Cosmology.
Astronomy Mathematics.
Cosmology.
Astronomy Mathematics.
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Dissertation
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1 online resource (ix, 115 pages) :
Department
Physics and Astronomy