A recent episode of the fascinating series 'Universe' (on the H2 channel) featured a look at what was claimed to be the largest superstructure in the cosmos: the cosmic web. This foam-like network linking normal material galaxies (amidst a vast 'sea' of dark matter) was singled out for scrutiny and said to exceed the scales of both galaxy clusters and superclusters.
An intriguing simulation, done by a group of astrophysicists calling itself "the Virgo Consortium" can be found here:
Note also the scale is not the same as one might believe. Though the Hubble expansion limit is often cited as about 13.7 billion light years, this only refers to the extent that the radiating objects, galaxies, clusters, quasars etc. occur within our light cone. However, owing to the actual expansion of space itself, registered as a "comoving distance", the universe is really some 93 billion light years in diameter, so the actual edge of the observable universe is some 46.5 b light years distant. This is important to realize because it gives an idea of the actual immensity of the cosmic web and its true scale size.
If readers will look closely at the simulation, they will also see the threadlike strands of the web which likewise appear in the cosmic sector shown in Fig. 1(b). above. The sector subtends about five hours (~ 75 deg) of Right Ascension. This is a cosmic snapshot of galaxy distribution obtained using the Two Degree (2dF) sky survey.
These thready filament-like stuctures convey the first hints that we are looking at a fractal cosmos. (For those who missed it, the nature of fractals themselves were the subject of an older blog, see, e.g. http://www.brane-space.blogspot.com/2009/11/some-basic-aspects-of-fractals.html ) One comparative aspect (comparing Figs. 1a and 1b) is immediately visible in the difference in void (i.e. darkish hole) distribution between the ideal and actual cosmic case. To fix ideas, the void in the ideal fractal sector is more or less uniformly distributed, at least around the circular stochastic element. In the real 2dF sector, the void is distributed toward the periphery of the field. There is much greater fractal density and complexity toward the center of the sector.
Early on, fractal researchers and investigators like Benoit Mandelbrot realized that fractal dimension, D, was not adequate to to accurately assess or determine the topology. A new measure was needed that reckoned in void extent, and that was defined by Mandelbrot as the lacunarity. One may define the lacunarity, L, to be:
L = Nr(k> R s) / R s- D
Now, the denominators for both are respectively, R s - D = (1) 2.5 = 1
Thus, the lacunarity is solely dependent on N, and for the real cosmic case, the ratio of it lacunarity to that of the abstract or ideal example is:
Lc / L = (105)/ 102 = 103
Thus, the number of voids is about 1000 times higher. This should not be astounding if one closely inspects 1B. Going through the sector we behold innumerable tiny white spaces , many more than in 1A. Again, for lacunarity, size of the voids is not the issue so much as the frequency of voids overall within the fractal structure.
What does all this have to do with parsing actual cosmic structure? Only that fractal analysis may be of some use in ferreting out the hidden dynamics of cosmic expansion, and in particular why interspatial topology alters the cosmic web in the vicinity of dark matter of certain densities and how this may allow us to estimate its actual fractal dimension and mass.
We may then be able to assert whether indeed the cosmic web is actually the largest superstructure, or not.