In physical cosmology, fractal cosmology is a set of minority cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is a fractal. More generally, it relates to the usage or appearance of fractals in the study of the universe and matter. A central issue in this field is the fractal dimension of the Universe or of matter distribution within it, when measured at very large or very small scales.

The use of fractals to answer questions in cosmology has been employed by a growing number of serious scholars close to the mainstream[citation needed], but the metaphor has also been adopted by others outside the mainstream of science, so some varieties of fractal cosmology are solidly in the realm of scientific theories and observations, and others are considered Fringe science, or perhaps metaphysical cosmology. Thus, these various formulations enjoy a range of acceptance and/or perceived legitimacy.

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,[1] 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 of about 2.[2] The ultimate significance of this result is not immediately apparent, but it seems to indicate that both randomness and hierarchal structuring are at work, on the scale of galaxy clusters and larger.

A debate still ensues, over whether the universe will become homogeneous and isotropic (or is smoothly distributed) at a large enough scale, as would be expected in a standard Big Bang or FLRW cosmology, and in most interpretations of the Lambda-CDM (expanding Cold Dark Matter) model. Scientific consensus interpretation is that the Sloan Digital Sky Survey suggests that things do indeed seem to smooth out above 100 Megaparsecs. Recent analysis of WMAP, SDSS, and NVSS data by a team from the University of Minnesota[3] shows evidence of a void around 140 Megaparsecs across, however, coinciding with the CMB cold spot, which, if confirmed, calls the assumption of a smooth universe into question. However there are serious hints that the apparent cold spot is a statistical artifact.

In May 2008, another paper[4] was published by a team including Pietronero, that concludes the large scale structure in the universe is fractal out to at least 100 Mpc/h. The paper asserts that the team has demonstrated that the most recent SDSS data shows "large amplitude density fluctuations at all scales" within that range, and that the data is consistent with fractality beyond this point, but inconsistent with a lower scale of homogeneity, or with predictions of large scale structure based solely on gravity. Their analysis shows the fractal dimension of the arrangement of galaxies in the universe (up to the range of 30 Mpc/h) to be about 2.1 (plus or minus 0.1).

However, an analysis of luminous red galaxies in the Sloane survey calculated the fractal dimension of galaxy distribution (on a scales from 70 to 100 Mpc/h) at 3, consistent with homogeneity; they also confirm that the fractal dimension is 2 "out to roughly 20 Mpc/h".[5]

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"[6] theory (see Chaotic inflation theory), in 1986. In this theory, the evolution of a scalar field creates peaks that become nucleation points which 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"[7] shows that this variety of Inflationary universe theory is still being seriously considered today. And inflation, in some form or other, is widely considered to be our best available cosmological model.

Since 1986, however, quite a large number of different cosmological theories exhibiting fractal properties have been proposed. And while Linde’s theory shows fractality at scales likely larger than the observable universe, theories like Causal dynamical triangulation[8] and Quantum Einstein gravity[9] 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 itself, and suggest that the dimensionality of space evolves with time. Specifically; they suggest that reality is 2-d at the Planck scale, and that spacetime gradually becomes 4-d at larger scales. French astronomer Laurent Nottale first suggested the fractal nature of spacetime in a paper on Scale Relativity published in 1992,[10] and published a book on the subject of Fractal Space-Time in 1993.[11]

French mathematician Alain Connes has been working for a number of years to reconcile Relativity with Quantum Mechanics, and thereby to unify the laws of Physics, using Noncommutative geometry. Fractality also arises in this approach to Quantum Gravity. An article by Alexander Hellemans in the August 2006 issue of Scientific American[12] 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 with physicist Carlo Rovelli[13] 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.

Publications

The book Discovery of Cosmic Fractals[14] by Yurij Baryshev and Pekka Teerikorpi gives an overview of fractal cosmology, and recounts other milestones in the development of this subject. It recapitulates the history of cosmology, reviewing the core concepts of ancient, historical, and modern astrophysical cosmology. The book also documents the appearance of fractal-like and hierarchal views of the universe from ancient times to the present. The authors make it apparent that some of the pertinent ideas of these two streams of thought developed together. They show that the view of the universe as a fractal has a long and varied history, though people haven’t always had the vocabulary necessary to express things in precisely that way.

Beginning with the Sumerian and Babylonian mythologies, they trace the evolution of Cosmology through the ideas of Ancient Greeks like Aristotle, Anaximander, and Anaxagoras, and forward through the Scientific Revolution and beyond. They acknowledge the contributions of people like Emanuel Swedenborg, Edmund Fournier D'Albe, Carl Charlier, and Knut Lundmark to the subject of cosmology and a fractal-like interpretation, or explanation thereof. In addition, they document the work of de Vaucoleurs, Mandelbrot, Pietronero, Nottale and others in modern times, who have theorized, discovered, or demonstrated that the universe has an observable fractal aspect.

On the 10th of March, 2007, the weekly science magazine New Scientist featured an article entitled "Is the Universe a Fractal?"[15] on its cover. The article by Amanda Gefter focused on the contrasting views of Pietronero and his colleagues, who think that the universe appears to be fractal (rough and lumpy) with those of David Hogg of NYU and others who think that the universe will prove to be relatively homogeneous and isotropic (smooth) at a still larger scale, or once we have a large and inclusive enough sample (as is predicted by Lambda-CDM). Gefter gave experts in both camps an opportunity to explain their work and their views on the subject, for her readers.

This was a follow-up of an earlier article in that same publication on August 21 of 1999, by Marcus Chown, entitled "Fractal Universe.".[16] Back in November 1994, Scientific American featured an article on its cover written by physicist Andrei Linde, entitled "The Self-Reproducing Inflationary Universe"[17] whose heading stated that "Recent versions of the inflationary scenario describe the universe as a self-generating fractal that sprouts other inflationary universes," and which described Linde's theory of chaotic eternal inflation in some detail.

In July 2008, Scientific American featured an article on Causal dynamical triangulation,[18] written by the three scientists who propounded the theory, which again suggests that the universe may have the characteristics of a fractal.

See also

Causal dynamical triangulation

Chaotic inflation theory

Hoag's Object

Holographic paradigm

Large scale structure

Nebular hypothesis

Scale invariance

Scale relativity

Self-organized criticality

Shape of the universe

References

^ Pieronero, L. (1987). "The Fractal Structure of the Universe: Correlations of Galaxies and Clusters". Physica A (144): 257.

^ Joyce, M.; Labini, F.S.; Gabrielli, A.; Montouri, M.; Pietronero, L. (2005). "Basic Properties of Galaxy Clustering in the light of recent results from the Sloan Digital Sky Survey". Astronomy and Astrophysics 443 (11). arXiv:astro-ph/0501583. Bibcode 2005A&A...443...11J. doi:10.1051/0004-6361:20053658.

^ Rudnick, L.; Brown, S.; Williams, L.. "Extragalactic Radio Sources and the WMAP Cold spot". ApJ 671 (1): 40–44. arXiv:0704.0908. Bibcode 2007ApJ...671...40R. doi:10.1086/522222.

^ Labini, F.S.; Vasilyev, N.L.; Pietronero, L.; Baryshev, Y. (2009). "Absence of self-averaging and of homogeneity in the large scale galaxy distribution". Europhys.Lett. 86. arXiv:0805.1132. Bibcode 2009EL.....8649001S. doi:10.1209/0295-5075/86/49001.

^ Hogg, David W.; Eisenstein, Daniel J.; Blanton, Michael R.; Bahcall, Neta A.; Brinkmann, J.; Gunn, James E.; Schneider, Donald P. (2005). "Cosmic homogeneity demonstrated with luminous red galaxies". The Astrophysical Journal 624: 54–58. arXiv:astro-ph/0411197. Bibcode 2005ApJ...624...54H. doi:10.1086/429084.

^ Linde, A.D. (August 1986). "Eternally Existing Self-Reproducing Chaotic Inflationary Universe". Physics Letters B.

^ Guth, Alan (22 June 2007). "Eternal inflation and its implications". J. Phys. A: Math. Theor. 40 (25): 6811–6826. arXiv:hep-th/0702178. Bibcode 2007JPhA...40.6811G. doi:10.1088/1751-8113/40/25/S25.

^ Ambjorn, J.; Jurkiewicz, J.; Loll, R. (2005). "Reconstructing the Universe". Phys.Rev. D 72. arXiv:hep-th/0505154. Bibcode 2005PhRvD..72f4014A. doi:10.1103/PhysRevD.72.064014.

^ Lauscher, O.; Reuter, M. (2005). Asymptotic Safety in Quantum Einstein Gravity. arXiv:hep-th/0511260. Bibcode 2005hep.th...11260L.

^ Nottale, Laurent (1992). "The theory of Scale Relativity". Intl. Journal of Modern Physics A 7 (20): 4899–4936.

^ Nottale, Laurent (1993). Fractal Space-time and Microphysics. World Scientific Press.

^ Hellemans, Alexander — The Geometer of Particle Physics — Scientific American - August, 2006

^ Connes, A.; Rovelli, C. (1994). "Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation". Class.Quant.Grav. 11: 2899–2918. arXiv:gr-qc/9406019. Bibcode 1994CQGra..11.2899C. doi:10.1088/0264-9381/11/12/007.

^ Baryshev, Y. and Teerikorpi, P. - Discovery of Cosmic Fractals - World Scientific Press (2002)

^ Gefter, Amanda - Is the Universe a Fractal? - New Scientist - March 10, 2007: issue 2594

^ Chown, Marcus - Fractal Universe - New Scientist - August 21, 1999

^ Linde, Andrei - The Self-Reproducing Inflationary Universe - Scientific American - November 1994 pp. 48-55

^ Ambjorn, J.; Jurkiewicz, J.; Loll, R. - The Self-Organizing Quantum Universe - Scientific American - July 2008 pp. 42-49

[*] Rassem,M. and Ahmed E., "On Fractal Cosmology", Astro. Phys. Lett. Commun. (1996), 35, 311.

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