Fractal cosmology
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In
physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of f ...
, fractal cosmology is a set of minority cosmological theories which state that the distribution of matter in the
Universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. ...
, or the structure of the universe itself, is a fractal across a wide range of scales (see also:
multifractal system A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed ...
). More generally, it relates to the usage or appearance of fractals in the study of the
universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. ...
and
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
. A central issue in this field is the
fractal dimension In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is me ...
of the universe or of matter distribution within it, when measured at very large or very small scales.


Fractals in observational cosmology

The first attempt to model the distribution of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987, and a more detailed view of the universe's large-scale structure emerged over the following decade, as the number of cataloged galaxies grew larger. Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a
fractal dimension In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is me ...
of about 2. The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3. The universe has been observed to be homogeneous and isotropic (i.e. is smoothly distributed) at very large scales, as is expected in a standard Big Bang or Friedmann-Lemaître-Robertson-Walker cosmology, and in most interpretations of the Lambda-Cold Dark Matter model. The scientific consensus interpretation is that the Sloan Digital Sky Survey (SDSS) suggests that things do indeed smooth out above 100 Megaparsecs. One study of the SDSS data in 2004 found "The power spectrum is not well-characterized by a single power law but unambiguously shows curvature ... thereby driving yet another nail into the coffin of the fractal universe hypothesis and any other models predicting a power-law power spectrum". Another analysis of luminous red galaxies (LRGs) in the SDSS data calculated the fractal dimension of galaxy distribution (on a scales from 70 to 100 Mpc/''h'') at 3, consistent with homogeneity, but that the fractal dimension is 2 "out to roughly 20 ''h''−1 Mpc". In 2012, Scrimgeour et al. definitively showed that large-scale structure of galaxies was homogeneous beyond a scale around 70 Mpc/''h''.


Fractals in theoretical cosmology

In the realm of theory, the first appearance of fractals in cosmology was likely with Andrei Linde's "Eternally Existing Self-Reproducing Chaotic Inflationary Universe" theory (see
chaotic inflation theory Eternal inflation is a hypothetical inflationary universe model, which is itself an outgrowth or extension of the Big Bang theory. According to eternal inflation, the inflationary phase of the universe's expansion lasts forever throughout most o ...
) in 1986. In this theory, the evolution of a scalar field creates peaks that become nucleation points that cause inflating patches of space to develop into "bubble universes," making the universe fractal on the very largest scales. Alan Guth's 2007 paper on "Eternal Inflation and its implications" shows that this variety of inflationary universe theory is still being seriously considered today. Inflation, in some form or another, is widely considered to be our best available cosmological model. Since 1986, quite a large number of different cosmological theories exhibiting fractal properties have been proposed. While Linde's theory shows fractality at scales likely larger than the observable universe, theories like
causal dynamical triangulation Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, is an approach to quantum gravity that, like loop quantum gravity, is background independent. This means that it does not assum ...
and the asymptotic safety approach to quantum gravity are fractal at the opposite extreme, in the realm of the ultra-small near the Planck scale. These recent theories of quantum gravity describe a fractal structure for
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
itself, and suggest that the dimensionality of
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually cons ...
evolves with
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...
. Specifically, they suggest that reality is 2D at the Planck scale, and that spacetime gradually becomes 4D at larger scales. French mathematician
Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vand ...
has been working for a number of years to reconcile general relativity with quantum mechanics using
noncommutative geometry Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions (possibly in some g ...
. Fractality also arises in this approach to quantum gravity. An article by Alexander Hellemans in the August 2006 issue of ''
Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...
'' quotes Connes as saying that the next important step toward this goal is to "try to understand how space with fractional dimensions couples with gravitation." The work of Connes and physicist Carlo Rovelli suggests that time is an emergent property or arises naturally in this formulation, whereas in causal dynamical triangulation choosing those configurations where adjacent building blocks share the same direction in time is an essential part of the "recipe." Both approaches suggest that the fabric of space itself is fractal, however.


See also

* Invariant set postulate * Large-scale structure of the Universe *
Scale invariance In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term ...
* Shape of the universe


Notes


References

*Rassem,M. and Ahmed E., "On Fractal Cosmology", Astro. Phys. Lett. Commun. (1996), 35, 311. {{DEFAULTSORT:Fractal Cosmology Astrophysics Fractals Physical cosmology