Fractal cosmology
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 across a wide range of scales (see also: multifractal system). 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.[1]
Fractals in observational cosmology
The first attempt to model the distribution of galaxies with a fractal pattern was made by
The universe has been observed to be homogeneous and
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".[4] 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".[5] In 2012, Scrimgeour et al. definitively showed that large-scale structure of galaxies was homogeneous beyond a scale around 70 Mpc/h.[6]
Fractals in theoretical cosmology
In the realm of theory, the first appearance of fractals in cosmology was likely with
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
French mathematician Alain Connes has been working for a number of years to reconcile general relativity with quantum mechanics 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[11] 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[12] suggests that time is an emergent property or arises naturally in this formulation, whereas in causal dynamical triangulation[9] 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
- Shape of the universe
Notes
References
- Rassem, M. and Ahmed E., "On Fractal Cosmology", Astro. Phys. Lett. Commun. (1996), 35, 311.