Emergence of Fractal Geometry in One-Dimensional Models of the Expanding Universe

ORAL

Abstract

Concentrations of matter in the universe, such as galaxies and galactic clusters, originated as very mall density fluctuations in the early universe. The primordial fluctuation spectrum is revealed by studies of the angular correlation of CMB across the sky with WMAP. The existence of super-clusters and voids suggests that a natural length scale for the matter distribution may not exist. A point of controversy is whether the distribution is fractal and, if so, over what range of scales. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. Even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one dimensional ``toy models'' we can overcome these limitations by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational field. Here we present the recent results of our ongoing investigation of the emergence of fractal geometry in one dimensional models of the expanding universe.

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Authors

  • Bruce Miller

    Texas Christian University

  • Jean-Louis Rouet

    Universite d'Orleans

  • Edward Fry

    Institute for Astronomy, ETH, National Optical Astronomy Observatory, Department of Physics, ETH, Texas A&M University, LANL, American Physical Society, Society of Physics Students National Office, Texas Tech University, University of Texas, Universite d'Orleans, Steward Observatory, University of Arizona, Texas A\&M University-Commerce, Texas A\&M University, Institute for Quantum Electronics, ETH Zurich, Department of Engineering and Applied Science, Harvard University, Rice University, University of Houston, Bucknell University, Department of Physics, Texas A\&M University, Air Force Research Laboratory, Department of Physics, Texas A\&M University, College Station, TX 77843, Department of Physics and MIC, Texas A\&M University, University of Texas at Arlington, Changwon National University, University of North Texas, Southwestern University, The Pennsylvania State University, University of Dallas, UT Southwestern Medical Center, Naval Air Systems Command, Institute for Quantum Studies and Department of Physics, Texas A\&M University, College Station, TX 77843, The University of Texas at Arlington, TCU, ELTE, National Institute of Chemistry, Ljubljana, Slovenia, Texas Christian University, Fort Worth, TX, Dept. of Physics, Texas A\&M University-Commerce, Univ. of North Texas, Los Alamos National Laboratory, Oswego State University of New York, Lee College, University of Texas at San Antonio, UTSA-Professor, UNT, Sam Houston State University, Sewanee: The University of the South, Director of Education for NSF, Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Sackler School of Chemistry, Tel-Aviv University, Rice University, Department of Physics and Astronomy, Houston, TX 77005, Center for Nonlinear Dynamics, University of Texas at Austin