Fractal cosmology

In physical cosmology, fractal cosmology relates to the usage or appearance of fractals in the study of the universe or cosmos. When cosmologists study the universe, they employ both observational and theoretical tools, and examine (or consider) the entire range of scale from the infinitesimal realm at the Planck scale to the ultimate size of the universe, even beyond the range of what is observable. In a wide variety of places, in fact almost anywhere they look in the universe, people studying the heavens are finding fractals or fractal-like structures. It is notable that fractals or fractality are encountered in both observational and theoretical cosmology, make an appearance at both extremes of the range of scale, and have been observed at various ranges in the middle. Similarly; the use of fractals to answer questions in cosmology has been employed by a growing number of serious scholars close to the mainstream, 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 that includes both extremes as well as the middle.

The utility of fractals

Since Benoit Mandelbrot coined the term fractal in 1975, to describe figures that are rough and varied rather than smooth or regular, the utility of the central concepts of Fractal Geometry have been an invitation to cosmologists. In "Fractals: form, chance, and dimension" (1977) he suggested that galaxies are fractally distributed, and gave a mathematical expression for such distributions. Mandelbrot’s landmark book "The Fractal Geometry of Nature" [Mandelbrot, Benoit B. — The Fractal Geometry of Nature — W.H. Freeman and Co. (1982)] followed up with a wealth of both new ideas, and tools whereby they might be put to use. Seeing that these tools allow one to mimic the appearance and properties of real-world forms like mountains, trees, and clouds much more easily than with conventional geometry, a number of scientists have sought to apply this new approach to solve problems in cosmology, and found many applications.

One of Mandelbrot's key insights, in the area of measurement, is quite relevant to cosmology and came about when he revisited the question first considered by Lewis Fry Richardson — "How long is the coast of Britain?" Richardson found that this number increased, as he used finer and more detailed maps. Noting that this relation also depended on the roughness of the terrain, he plotted this for various locations to yield a fractional exponent. Mandelbrot thought this result was especially significant, and suggested that it means the coastline actually has a fractional dimension (see Fractal dimension) which varies with the character of the terrain under study, giving us a measure of its roughness. By regarding this idea of fractional dimension as a measuring tool for physical reality, as well as an attribute of certain mathematical objects and spaces, he began a revolution.

Fractals in observational cosmology

In the observational realm, the fractal distribution of galaxies was first demonstrated to fit the astronomical data accurately by Luciano Pietronero and his team in 1987 [Pietronero, L. — The Fractal Structure of the Universe: Correlations of Galaxies and Clusters... — Physica A 144, 257 (1987)] , and a more detailed view of fractality in the universe’s large-scale structure emerged over the following decade, as the number of cataloged galaxies grew larger. The universe shows a definite fractal aspect (according to Pietronero and his colleagues), over a fairly wide range of scale, with a fractal dimension of about 2 [Joyce, M.; Labini, F.S.; Gabrielli, A., Montouri, M.; Pietronero, L. — Basic properties of galaxy clustering...SDSS — arXiv:astro-ph/0501583v2] . 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. Scientists favoring the mainstream view have observed 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 [Rudnick, L.; Brown, S.; Williams, L. - Extragalactic Radio Sources and the WMAP Cold spot - arXiv:0704.0908v2] shows evidence of a void around 140 Megaparsecs across, however, coinciding with the CMB cold spot, which again calls the assumption of a smooth universe into question.

In May of 2008, another paper [Labini, F.S.; Vasilyev, N.L.; Pietronero, L.; Baryshev, Y. - The large scale inhomogeneity of the galaxy distribution - arXiv: 0805.1132v1] 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).

Fractals in theoretical cosmology

In the realm of theory (apart from Mandelbrot’s ideas), the first appearance of fractals in cosmology was likely with Andrei Linde’s "Eternally Existing Self-Reproducing Chaotic Inflationary Universe" [Linde, A.D. - Eternally Existing Self-Reproducing Chaotic Inflationary Universe - Physics Letters B - August 1986] 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" [Guth, Alan — Eternal inflation and its implications — arXiv:hep-th/0702178] 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 [Ambjorn, J.; Jurkiewicz, J.; Loll, R. - Reconstructing the Universe - arXiv/hep-th/0505154] and Quantum Einstein gravity [Lauscher, O.; Reuter, M. — Asymptotic Safety in Quantum Einstein Gravity — arXiv:hep-th/0511260] 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 [Nottale, Laurent - The theory of Scale Relativity — Intl. Journal of Modern Physics A, Vol. 7, No. 20 (1992) 4899-4936] , and published a book on the subject of Fractal Space-Time in 1993 [Nottale, Laurent - Fractal Space-time and Microphysics.. — World Scientific Press (1993)] .

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 [Hellemans, Alexander — The Geometer of Particle Physics — Scientific American - August, 2006] 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 [Connes, A.; Rovelli, C. - Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation... Class.Quant.Grav. 11 (1994) 2899-2918 arXiv:gr-qc/9406019] 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.

In recent years, one individual who has been especially influential in this area is M. S. El Naschie. He is Editor in Chief of an academic Journal called "Chaos, Solitons, and Fractals," which has included papers by numerous authors including Nottale, of theoretical work where Fractals are employed to explain or derive the laws of Physics, and many of these papers relate directly to Cosmology. El Naschie has sought to foster conversation between scientists from various disciplines, for the purpose of increasing the scope or palette of choices under consideration. He has also published numerous papers on related topics himself, as his E-Infinity [El Naschie, M. S. — A review of E infinity theory and the mass spectrum of high energy particle physics — Chaos, Solitons, and Fractals: vol. 19, is. 1 (January, 2004)] theory predicts a Cantorian fractal space-time, and derives the masses of the known subatomic particles thereby. The book "Space Time Physics and Fractality," [Weibel, P.; Ord, G.; Rössler, O.; editors — Space Time Physics and Fractality: Festschrift in Honour of..: Springer Wien New York (2005)] published in 2005, is a 'tour de force' of papers on the subject by a number of scientists and mathematicians, and is dedicated to El Naschie in honor of his 60th birthday.

Cosmic fractals book documents evolution of field

The book Discovery of Cosmic Fractals [Baryshev, Y. and Teerikorpi, P. - Discovery of Cosmic Fractals - World Scientific Press (2002)] by Yurij Baryshev and Pekka Teerikorpi recapitulates the entire history of cosmology, thoroughly reviewing the core concepts of ancient, historical, and modern astrophysical cosmology, and they also document the evolution 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 evolved together. They clearly show that the view of the universe as a fractal has quite 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 evolution of 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.

cience periodicals have featured this subject

On the 10th of March, 2007, the weekly Science magazine New Scientist featured an article entitled "Is the Universe a Fractal?" [Gefter, Amanda - Is the Universe a Fractal? - New Scientist - March 10, 2007: issue 2594] on its cover. The article by Amanda Gefter focused on the contrasting views of Pietronero and his colleagues, who favor the view that the universe appears to be fractal (rough and lumpy) with those of David Hogg of NYU and others who believe strongly 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." [Chown, Marcus - Fractal Universe - New Scientist - August 21, 1999] However, the seeds of the fractal universe concept were planted in the minds of Science readers long before that. Back in November of 1994, Scientific American featured an article on its cover written by physicist Andrei Linde, entitled "The Self-Reproducing Inflationary Universe" [Linde, Andrei - The Self-Reproducing Inflationary Universe - Scientific American - November 1994 pp. 48-55] 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 of 2008, Scientific American featured an article on Causal Dynamical Triangulation [Ambjorn, J.; Jurkiewicz, J.; Loll, R. - The Self-Organizing Quantum Universe - Scientific American - July 2008 pp. 42-49] , written by the three scientists who propounded the theory, which again suggests that the universe may be fractal. The subject of fractals in cosmology has been a popular topic for both scientists and science writers, during that entire span of time.

References

ee also

External links

* [http://www.cosmology.info/2005conference/index.html 1st Crisis in Cosmology conference] included several talks on Fractals in Cosmology
* [http://www.cosmology.info/2008conference/index.html 2nd Crisis in Cosmology conference] more presentations on fractals in the cosmos
* [http://www.fractaluniverse.org/ Colin Hill's Fractal Universe site]
* [http://www.fractalcosmology.com/ Yun Pyo Jung's Fractal Cosmology site]
* [http://www.amherst.edu/~rloldershaw/menu.html Robert Oldershaw's Fractal Cosmology page]
* [http://www.fractalcosmos.com Harry Schmitz's Fractal Cosmos page]
* [http://www.nrao.edu/pr/2007/coldspot/ NRAO Press release on giant void]
* [http://arxiv.org/find/all/1/all:+fractal/0/1/0/all/0/1 Search on arXiv.org for papers containing "fractal"] includes a high percentage of papers relevant to Cosmology
* [http://arxiv.org/abs/astro-ph/0406202v1 Statistical physics for complex cosmic structures] by L. Pietronero and F. Sylos Labini
* [http://arxiv.org/abs/astro-ph/0505185 Fractal Approach to Large-Scale Galaxy Distribution] by Y. Baryshev and P. Teerikorpi
* [http://arxiv.org/abs/0805.1132 The large scale inhomogeneity of the galaxy distribution] May '08 paper by Labini, Vasilyev, Pietronero, and Baryshev
* [http://en.wikiversity.org/wiki/Infinite_Hierarchical_Nesting_of_Matter Fractals as nesting of matter (translation of Russian Wikipedia page)]
* [http://www.luth.obspm.fr/~luthier/nottale/LIWOS7-1cor.pdf "Scale-Relativity and Cosmology"] from Fractal Space-time and Microphysics by Laurent Nottale