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 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 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.
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 FLRW cosmology, and in most interpretations of the Lambda-Cold Dark Matter model. 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 Mpc/h".
In 2013, astronomers discovered a large quasar group (LQG) that is 1.6 billion light-years in diameter, far larger than allowed by the cosmological principle, which asserts that the universe should be homogeneous at scales this large.
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