How Was the Cosmic Web Discovered and How Do Psuedo Polyhedrons Relate to It?
Scientists drive to understand the origins of our Universe is one of the most compelling known to man. How did everything we see around us come into being? Theology and science both make attempts to answer this question. For this article, lets explore the scientific aspects and see how we came about our current understanding of the Universe, the Cosmic Web.
Origins and Geometries
The Big Bang is science’s best theory as to the start of our Universe. That along has so much complexity that another article would be needed to comprehend all it entails. From the Big Bang does all we see spring forth, with matter slowly congregating into stars, galaxies, and all that is contained within and without them. According to most work, the Universe should be homozygous, or that on grand scales everything should look the same. Why would physics operate differently in separate regions of the Universe?
So, imagine everyone’s surprise when in 1981 Robert Kirshner, Augustus Oemler, Paul Schechter, and Stephen Schectman discovered a million cubic megaparsec (meaning roughly a cube with 326 mega light-years (MLY) for each side) void in space in the direction of Bootes. Well, when we said void here we are pointing out the relative lack of anything in it with only 4% of the galactic content such a space should have. Velocity readings from redshift data indicated that the void was moving at a rate of 12,000 to 18,000 kilometers per second away from us, not too shocking in an expanding Universe. Behind the void (which is moving at less than 9,000 kilometers per second away from us) is a grouping of galaxies about 440 MLYs away and beyond the void (which is moving at more than 21,000 kilometers per second away from us) is another grouping of galaxies about 1,020 MLYs. The overall appearance is that the void is like a cell caved out of space (Gott 71-2).
For Yakov Zeldovich, this was no surprise. A Soviet astrophysicist who also worked on their nuclear program, he did much work on the circumstances that forced the Universe to grow and evolve. One particular aspect he pushed for was adiabatic fluctuations, or when changes in the density of thermal radiation corresponded to changes in density of matter arising from correlations in photons, electrons, neutrons and protons. This would be true if there was more matter than antimatter just after the Big Bang, if the thermal radiation was dominant at the same time, and if both arose from massive particle decay. The consequences of this would be large clustering of material prior to the first galaxies with some excess energy density present known as gravity. This caused the ellipsoid material to flatten out into what became known as Zeldovich pancakes or “high density surfaces formed by gravity” with a thickness approaching zero (66-7).
Zeldovich along with Jaan Einasto and Sergei Shandarin found that such conditions extended on a large scale would make a Voronoi Honeycomb. Like the name implies, it has similarities to a bee hive, with lots of empty spaces with random walls all connected. The voids themselves would be separated from one another. So why specify as a Voronoi variety? It pertains to that field of geometry, where points are assigned as being equidistant from arbitrary centers and fall on planes that are perpendicular to the line connecting the centers and also bisects said line. This has the effect of creating irregular polyhedral, and the scientists work showed how galaxies would reside on those planes with greater concentrations at the vertices of planes. This would mean evidence would appear as filaments that seem to connect galaxies and large voids, just like the one found in the direction of Bootes (Gott 67-70, Einasto, Parks).
But this void that was found was not the only clue that perhaps the Zeldovich pancakes and Voronoi Honeycombs were a reality. The Virgo Supercluster was found to have a flat geometry like a pancake according to work by Gerard de Vaucouleurs. Observations by Francis Brown from 1938 to 1968 looked at galactic alignments and found non-random patterns to them. A followup in ’68 by Sustry showed galaxy orientations were not random but that elliptical galaxies were in the same plane as the cluster they belonged to. A 1980 paper by Jaan Ernasto, Michkel Joeveer, and Enn Saar looked at redshift data from the dust around galaxies and found that “straight chains of clusters of galaxies” were seen. They also uncovered how “planes joining neighboring chains are also populated by galaxies.” This all excited Zeldovich and he pursued these clues further. In a 1982 paper with Ernasto and Shandarin, Zeldovich took further redshift data and plotted various groupings of galaxies in the Universe. The mapping showed many empty spaces in the Universe with seemingly higher concentrations of galaxies forming walls to the voids. On the average, each void was a 487 MLYs by 487 MLYs by 24 MLYs in volume. The Pisces-Cetus Supercluster Complex was also analyzed in the late 1980s and found to have filament structuring to it (Gott 71-2, West, Parks).
Another piece of evidence was provided by computer simulations. At the time, computing power was growing fast and scientists were finding the applications in modeling complex scenarios with them to extrapolate how theories actually played out. In 1983, A.A. Klypin and S.F. Shandarin run their own, with some conditions. They use a 778 MLY3 cube with 32,768 particles that had density changes in accordance with adiabatic fluctuations. Their simulation found that large scale “lumpiness” was seen but small scaling of the structures wasn’t seen, with fluctuations smaller than a wavelength of 195 MLY resulting in the mechanics that Zeldovich predicted. That is, the pancakes formed and then networked with each other, forming threads connecting them filled with clusters (Gott 73-5).
Further evidence for the emerging structure of the Universe came from cross sections of 6 degrees each taken of the sky in 1986. Using the Hubble Law for recessional velocities, a furthest distance of 730 mega light years was found in each section, which had filaments, voids and branches that were consistent with Zeldovich’s model. The edges of these features were curved around geometries approximating those of Richard J. Gott, who in his high school days discovered a new class of polyhedral. He started by “layering polyhedra” using truncated octahedrons. If you stack them so that the truncated portions fit into each other, you end up with a body-centered cubic array which as it turns out has some applications in X-ray diffraction of metallic sodium. Other shapes were possible to utilize besides the octahedrons. If one joined 4 truncated hexahedrons in just the right manner, you could get a saddle-shaped surface (that is, a negative-curvature where the degree measure of a triangle resting on it would total less than 180) (106-8, 137-9).
One can also get a positive curvature surface too via approximations of polyhedral. Take a sphere, for example. We can choose many approximations for it, such as a cube. With three right angles meeting at any given corner, we get a degree measure of 270, 90 less than needed to have a plane. One can imagine choosing more complex shapes to approximate the sphere, but it should be clear that we will never get to that 360 needed. But those hexahedrons from earlier have a 120-degree corner for each, meaning that the angle measure for that particular vertex is 480. The trend is apparent now, hopefully. Positive curvature will result in a vertex with less than 360 but negative curvature will be more than 360 (109-110).
But what happens when we lay with both of these at the same time? Gott found that if you remove the square faces from the truncated octahedrons, you get roughly hexagonal vertices, resulting in what he described as a “holey, spongy surface” which exhibited bilateral symmetry (much like your face does). Gott had uncovered a new class of polyhedral because of the open spaces but with unlimited stacking. They were not regular polyhedra because of those openings nor were they regular planar networks because of the infinite stacking features. Instead, Gott’s creation had features of both and so he dubbed them pseudopolyhedra (110-5).
How It All Comes Down to the (Near) Beginning
Now the reason this new class of shape is relevant to the structure of the Universe comes from many clues scientists have been able to gleam. Observations of galactic distributions made their alignments similar to the pseudopolyhedra vertices. Computer simulations using known inflation theory and the densities of energy and matter show that the sponges from the new geometry come into play. This was because high density regions stopped expanding and collapsed, then clustered together while low density spread out, creating the gatherings and voids scientists see in the Cosmic Web. We can think of that structure as following pseudopolyhedra in its overall pattern and perhaps extrapolate some unknown features of the Universe (116-8).
Now we know that these fluctuations involving photons, neutrons, electrons, and protons helped lead to these structures. But what was the driving force behind said fluctuations? That is our old friend inflation, the cosmological theory that explains many of the Universes properties we see. It allowed for pieces of the Universe to fall out of causal contact as space expanded at a highly accelerated rate, then decelerated as the energy density propelling inflation was countered by gravity. At the time, the energy density for any given moment was applied in x-y-z directions, so any given axis experienced 1/3 the energy density at the time, and a part of that was thermal radiation or photonic movement and collisions. Heat helped drive the expansion of the Universe. And their movement was restricted to the space provided to them, so regions that were not casually connected to this didn’t even feel its effects until casual connections were reestablished. But recall I mentioned earlier in this article how the Universe is rather homogenous. If different places of the Universe experience thermal conditioning at different rates, then how did the Universe achieve thermal equilibrium? How do we know that it did? (79-84)
We can tell because of the cosmic microwave background, a relic from when the Universe was 380,000 years old and photons were free to travel space unencumbered. All over this remnant we find the temperature of the shifted light to be 2.725 K with only a 10 millionth a degree error possible. That’s pretty uniform, to the point where those thermal fluctuations we expected shouldn’t have happened and so the model of the pancakes that Zeldovich shouldn’t have happened. But he was clever, and did find a solution to match the data seen. As different pieces of the Universe reestablished casual contact, their changes in temperature were within 100 millionths a degree and that amount above/below could be enough to account for the models we see. This would become known as the Harrison-Zeldovich scale-invariant spectrum, for it showed that the magnitude of the changes wouldn’t prevent the fluctuations required for galactic growth (84-5).
Einasto, Jaan. “Yakov Zeldovich and the Cosmic Web Paradigm.” arXiv: 1410.6932v1.
Gott, J., Richard. The Cosmic Web. Princeton University Press, New Jersey. 2016. 67-75, 79-85, 106-118, 137-9.
Parks, Jake. "At the Edge of the Universe." Astronomy. Mar. 2019. Print. 52.
West, Michael. “Why Do Galaxies Align?” Astronomy May 2018. Print. 48, 50-1.
Questions & Answers
© 2019 Leonard Kelley