Primordial fractal density perturbations and structure formation in the universe: One-dimensional collisionless sheet model

Takayuki Tatekawa, Keiichi Maeda

    Research output: Contribution to journalArticle

    19 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)531-544
    Number of pages14
    JournalAstrophysical Journal
    Volume547
    Issue number2 PART 1
    DOIs
    Publication statusPublished - 2001 Feb 1

    Fingerprint

    fractals
    universe
    perturbation
    horizon
    galaxies

    Keywords

    • Cosmology: theory
    • Large-scale structure of universe

    ASJC Scopus subject areas

    • Space and Planetary Science

    Cite this

    Primordial fractal density perturbations and structure formation in the universe : One-dimensional collisionless sheet model. / Tatekawa, Takayuki; Maeda, Keiichi.

    In: Astrophysical Journal, Vol. 547, No. 2 PART 1, 01.02.2001, p. 531-544.

    Research output: Contribution to journalArticle

    @article{450a7f7b930d4dad889a1e786ca7115b,
    title = "Primordial fractal density perturbations and structure formation in the universe: One-dimensional collisionless sheet model",
    abstract = "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.",
    keywords = "Cosmology: theory, Large-scale structure of universe",
    author = "Takayuki Tatekawa and Keiichi Maeda",
    year = "2001",
    month = "2",
    day = "1",
    doi = "10.1086/318392",
    language = "English",
    volume = "547",
    pages = "531--544",
    journal = "Astrophysical Journal",
    issn = "0004-637X",
    publisher = "IOP Publishing Ltd.",
    number = "2 PART 1",

    }

    TY - JOUR

    T1 - Primordial fractal density perturbations and structure formation in the universe

    T2 - One-dimensional collisionless sheet model

    AU - Tatekawa, Takayuki

    AU - Maeda, Keiichi

    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 -