The Cosmic Web
The original text is from 2016, but this review is written on the occasion of the unaltered paperback version in 2018. Gott sketches the successive cosmological models that were designed to understand why the universe is behaving the way it does. The description is intended to be understood by anyone interested but what is so nice about reading this ongoing evolution of our insights is that he has known as a young researcher the people who were working on earlier models, and he has contributed himself in his later career. This makes his account very personal. His main interest involves the structure of the universe at very large scale. The galaxies are not uniformly distributed, but they cluster on filaments and form a sponge-like web, The term "web" was first introduced in 1983 in a paper by Klypin and Shandarin. This is the story of the universe told at the mind-blowing scale of billions and trillions of light-years.
The story starts with the models of the 20th century. Using red-shifts, Hubble showed that the universe is currently expanding. Another debate was about the cosmological constant and its value which defined the shape (flat, hyperbolic or elliptic) of our universe. Only near the end of the century it was observed that the universe is not only expanding, but that the expansion was accelerating.
Fritz Zwicky contributed to the larger structure studying clusters of galaxies, using gravitational lensing. In the course of this research, some effects could only be explained using a smooth massive presence which is now called dark matter.
Gott himself enters the scene with his research about the possible ways that galaxies are formed and to what they evolve. Two competing possible structures are considered: either the galaxies cluster together and float like isolated meatballs in a mostly empty cosmic soup or they fill up the universe, but leaving large, almost vacuum holes like a Swiss cheese. The clustering depends on perturbations in the initial conditions of the universe and which of both models will result (the soup or the cheese) depends on whether the density is considered low or high. Zeldovich in the USSR considered a Swiss cheese model where galaxies cluster on relatively thin boundaries of some vacuum 3D Voronoi cells
The observed uniformity in the microwave background (how we observe the early universe) remained an enigma for some time. Uniformity can only be explained if the whole cosmos had been in a contact close enough to exchange photons, but what we observe is that they are too far apart to have ever met. This can only be solved by accepting an inflationary phase right after the Big Bang when space expanded faster than light, doubling in size every 10−38
seconds. Thus parts escaped outside our causality horizon and only now, because the expansion has slowed down to below light-speed, they re-enter our causality horizon. So they look like being too far apart, but they were actually very close and in causal contact before the inflation. This explanation for the horizon problem can be understood by realizing that one second after the Big Bang we can only see what is less than one light-second away, but as time continues, we can see farther and also see objects that are much farther apart.
The expansion during the high energy inflation period gave rise to bubbles of lower energy. Such a bubble creates a universe on its own, and since there are more bubbles, this assumption becomes a possible multiverse model, our universe being in one of these bubbles. The formation of galaxies could be explained by assuming cold dark matter that can clump together spontaneously by gravitation. The next question is how these galaxies are distributed and how they will evolve. What follows is a remarkable story of Gott's high school project on regular space filling polyhedral structures. He detected that by removing some faces to connect all the polyhedral interiors but at the same time leaving all the remaining faces connected too, he got some sponge-like space filling surface. For example a truncated octahedron consists of 8 hexagonal faces and 6 square faces (where the vertices of the octahedron are truncated). These polyhedra can fill 3-space. Now remove all the square faces from the structure, and one gets a sponge-like surface that is neither a soup-with-meatballs models (where the meatballs are disconnected) or the cheese-with-holes model (where the holes are disconnected). All the remaining faces and all the empty space of the octahedral tessellation are connected. Thus 3D space is partitioned in two disjunct yet fully connected subsets like in a sponge. Gott defined the genus of such a surface as the number of holes minus the number of isolated regions of matter. It is equal to the integral of the curvature and equals minus half the Euler characteristic (g=-(V-E+F)/2). The genus is negative for the Swiss cheese model and positive for the meatball model and anything in between is sponge-like.
But the sponge-like distribution of galaxies is only temporally. Galaxies may be attracted to each other too. One may in fact construct fluid flow lines showing how galaxies and clusters of galaxies are attracted to so called super clusters. We are with our solar system in the Milky Way, part of a Local Group, belonging to the Virgo Supercluster, which is a branch of the Laniakea Supercluster. Like the water in the watershed of a river we are attracted to the center of the Laniakea. Laniakea means immeasurable heaven in Hawaiian.
Simulations were run and observations were made detecting clusters of galaxies arranged in filaments. So the sponge became a web. The term "cosmic web" was used first in the title of a paper by Bond, Kofman, and Pogosyan "How filaments are woven into the cosmic web" that they posted in 1995 on arXiv.
The iconic elliptic map of the cosmic background radiation (CBR) is a projection of the celestial sphere showing the radio spectrum observed by the WMAP satellite. Investigation of the curvature of the isothermal contour lines can be used to define the genus of the topology. It showed that this matched the sponge-like structure that was also predicted in the simulations when starting from random quantum fluctuations during the inflation.
Still one element is missing to explain the acceleration of the expansion of the universe detected in 1995. This is explained by the repulsive effect of a negative pressure from some energy density. However since the gravitational effect of matter density is much higher than the effect of energy density, one needs an enormous amount of energy to explain the acceleration. To match all the observations, one came to a consensus in 2015 that it is required that about 70% of the universe should consist of dark energy and only 30% of matter, most of which is dark matter. As the universe increases, the density of matter will decrease, and the energy density will increase. Current estimates are that the size is currently doubling every 12.2 billion years. Depending on the ratio of the pressures caused by dark energy and dark matter, different scenarios for the ultimate future of the universe in a googol or a googolplex years are proposed.
The particularly nice thing about the way Gott tells this story is that he can tell it because he personally contributed to it and met or collaborated with many of the other people who have shaped our current knowledge of the cosmos. Moreover he not only describes the models but he also explains why new observations made it necessary to modify a previous model. So he explains not not only the "what" but also the "why". Of course he is not showing the field equations, that would be too technical beyond the understanding of a general reader, but he explains what the different interpretation is of a constant placed on the left-hand side or the right-hand side of the equations. He also gives physical and mathematical information about the phenomena discussed. His topological science project is explained in some detail with classic polyhedra, and we can follow his derivation of the genus of a sponge-like structure and we learn the meaning of curvature. He mentions the use of the Mollweide equal area projection to picture the CBR. There are Gaussian and other curves (like many other graphics) throughout the book. Sixteen colour plates are bundled at the end, like some extra notes to the different chapters and references to the literature. Also the subject and name index is quite effective. This is a very readable account of how our understanding about the cosmos has evolved with some interesting mathematical excursions. In particular the web-like structure at an incredible large scale is very well explained, which fully justifies the title of the book.