TY - JOUR
T1 - Primordial fractal density perturbations and structure formation in the universe
T2 - One-dimensional collisionless sheet model
AU - Tatekawa, Takayuki
AU - Maeda, Kei Ichi
PY - 2001/2/1
Y1 - 2001/2/1
N2 - The two-point correlation function of galaxy distribution shows that structure in the present universe is scale-free up to a certain scale (at least several tens of 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 an Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will result. 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.
AB - The two-point correlation function of galaxy distribution shows that structure in the present universe is scale-free up to a certain scale (at least several tens of 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 an Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will result. 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.
KW - Cosmology: theory
KW - Large-scale structure of universe
UR - http://www.scopus.com/inward/record.url?scp=0035255418&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035255418&partnerID=8YFLogxK
U2 - 10.1086/318392
DO - 10.1086/318392
M3 - Article
AN - SCOPUS:0035255418
VL - 547
SP - 531
EP - 544
JO - Astrophysical Journal
JF - Astrophysical Journal
SN - 0004-637X
IS - 2 PART 1
ER -