Fractal cosmology

A 'galaxy of galaxies' from the Mandelbrot Set

Fractal Cosmology is a term in Physical cosmology which 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. 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. Likewise; 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, which places some varieties of Fractal Cosmology in the realm of Fringe science, or perhaps Metaphysical cosmology. 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. Mandelbrot’s landmark book The Fractal Geometry of Nature was chock full 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, scientists have sought to apply this new approach to solve problems in cosmology, and found many applications. One of Mandelbrot's key insights, in this area, 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. 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, 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 definitely shows a fractal aspect, over a fairly wide range of scale, with a fractal dimension of about 2. A debate still ensues, over whether the universe will become homogeneous and isotropic (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 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.

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 Self Reproducing Chaotic Inflationary Universe theory in 1986. In this theory, the evolution of a scalar field causes inflating patches of space that become nucleation points for "bubble universes," making the universe fractal on the largest scales. And Alan Guth's '07 paper on Eternal Inflation shows that this variety of Inflationary universe theory is still being seriously considered today. 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 larger than the observable universe, theories like Causal dynamical triangulation and Quantum Einstein gravity are fractal at the opposite extreme, in the realm of the ultra-small near the Planck scale. These 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 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, and published a book on the subject of Fractal Space-Time in 1993.

Cosmic Fractals book documents evolution of field

The book Discovery of Cosmic Fractals by Yurij Baryshev and Pekka Teerikorpi recapitulates the entire history of cosmology, thoroughly reviewing the core concepts of modern cosmology, and documenting the evolution of fractal-like views of the universe from ancient times to the present. They 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 quite that way. In addition, they document the work of Pietronero and others in modern times, who have discovered or demonstrated that the universe has an observable fractal aspect.

Science 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?" 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). This is a follow-up of an earlier article in that same publication on August 21 of 1999, by Marcus Chown, entitled "Fractal Universe." 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" 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.

See also

Astronomy Astrophysics Benoît Mandelbrot Causal dynamical triangulation Cosmology Fractal

Galaxy History of physics Large scale structure Nebular hypothesis Olbers' paradox Physical cosmology

Renormalization group Scale invariance Scale relativity Self-organized criticality Universe

External Links

• Robert Oldershaw's Fractal Cosmology page
• Colin Hill's Fractal Universe site
• 1st Crisis in Cosmology conference which included several talks on Fractals in Cosmology
• Yun Pyo Jung's Fractal Cosmology site
• NRAO Press release on giant void
• Search on arXiv.org for papers containing "fractal" which includes a high percentage of papers relevant to cosmology
• Statistical physics for complex cosmic structures - L. Pietronero and F. Sylos Labini
• Fractals as nesting of matter (translation of Russian Wikipedia page)