Astronomy and Astrophysics – Astrophysics
Scientific paper
2000-03-09
Astrophys.J. 547 (2001) 531-544
Astronomy and Astrophysics
Astrophysics
17 pages, 19 jpeg figures. Accepted for publication in ApJ. Figures are also available from http://www.phys.waseda.ac.jp/gra
Scientific paper
10.1086/318392
Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze the time evolution of fractal density perturbations in Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will come out. We assume a one-dimensional collisionless sheet model with initial Cantor-type fractal perturbations. The nonlinear structure seems to approach some attractor with a unique fractal dimension, which is independent of the fractal dimensions of initial perturbations. A discrete self-similarity in the phase space is also found when the universal nonlinear fractal structure is reached.
Maeda Kei--ichi
Tatekawa Takayuki
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