Just as stars form from inhomogeneities in interstellar clouds, galaxies, galaxy clusters, and larger structures are believed to have grown from small density fluctuations in the matter of the expanding universe. 
(Sec. 19.1) Given the conditions in the universe during the atomic and galactic epochs (Table 27.1), cosmologists calculate that regions of higher-than-average density that contained more than about a million times the mass of the Sun would have begun to contract. There was thus a natural tendency for million—solar mass "pregalactic" objects to form. In Chapter 24 we saw a little of how these pregalactic fragments might have interacted and merged to form galaxies. (Sec. 24.4) Here, we concern ourselves mostly with the formation of structure on much larger scales.
By the early 1980s, cosmologists had come to realize that galaxies could not have formed from the contraction of inhomogeneities involving only normal matter. The following lines of reasoning led to this conclusion:
(Sec. 26.6)
(Sec. 25.6)
Put another way, if galaxies had grown from density fluctuations in the normal-matter component of the early universe, then the fluctuations would have had to be so large as to leave a clearly observable imprint on the cosmic microwave background. That imprint is not observed.
Fortunately for cosmology, the fact that most of the universe is made of dark matter, which has properties very different from those of normal matter, provides an alternative explanation for the large-scale structure we see today. Whatever its true nature, dark matter interacts only very weakly with normal matter and radiation. As a result, the density of initially high-density regions of dark matter has been increasing ever since matter first began to dominate the universe at a redshift of about 20,000. Thus, point 1 of our list does not apply because the dark matter started clumping well before decoupling (redshift 1500). Furthermore, because the dark matter is not directly tied to the radiation, dark-matter density inhomogeneities could have been quite large at the time of decoupling without having a correspondingly large effect on the microwave background, so the constraints of point 2 are also avoided. In short, dark matter could clump to form large-scale structure in the universe without running into the problems just described for normal matter.
In this picture (Figure 27.14), dark matter determines the overall distribution of mass in the universe and clumps to form the observed large-scale structure without violating any observational constraints on the microwave background. Then, at later times, normal matter is drawn by gravity into the regions of highest density, eventually forming galaxies and galaxy clusters. This picture explains why so much dark matter is found outside the visible galaxies. The luminous material is strongly concentrated near the density peaks and dominates the dark matter there, but the rest of the universe is essentially devoid of normal matter. Like foam on the crest of an ocean wave, the universe we see is only a tiny fraction of the total.
Figure 27.14 The formation of structure in the cosmos. (a) The universe started out as a mixture of (mostly) dark and normal matter. (b) A few thousand years after the Big Bang, the dark matter began to clump. (c) Eventually the dark matter formed large structures (represented here by the two high-density peaks) into which normal matter flowed, ultimately to form the galaxies we see today. The three frames at right represent the densities of dark matter (red) and normal matter (yellow) graphed at left.
Given that the nature of the dark matter is still unknown, theorists have considerable freedom in choosing its properties when they attempt to simulate the formation of structure in the universe. Cosmologists distinguish between two basic types of dark matter on the basis of its temperature at the time when galaxies began to form. These types are known as hot dark matter and cold dark matter, respectively, and they lead to quite different kinds of structure in the present-day universe.
Hot dark matter consists of lightweight particles—much less massive than the electron. If neutrinos turn out to have a small mass, as now appears to be the case, they may be leading candidates for hot dark-matter particles. Simulations of a universe filled with hot dark matter indicate that large structures, such as superclusters and voids, form fairly naturally, but the computer models cannot account for the existence of structure on smaller scales. Small amounts of hot material tend to disperse, not clump together. Attempts to produce galaxies and clusters by other means after the formation of larger objects have been only partly successful, and most cosmologists have concluded that models based purely on hot dark matter are unable to explain the observed structure of the universe.
Cold dark matter consists of very massive particles, possibly formed during the GUT era or even before. Computer simulations modeling the universe with these particles as the dark matter easily produce small-scale structure. With the understanding that galaxies form preferentially in the densest regions, and with some fine-tuning, these models can also be made to produce large-scale structure comparable to what is actually observed.
Perhaps the best results to date (that is, the results that agree most closely with observations) come from calculations in which a mixture of hot and cold dark matter is assumed. Figure 27.15 shows the results of a supercomputer simulation of a mixed-dark-matter universe. Compare these images with the real observations of nearby structure shown in Figures 24.33 and 24.34. Although calculations like this cannot prove that dark-matter models are the correct description of the universe, the similarities between the models and reality are certainly very striking.
Figure 27.15 Successively magnified views of a 100 
100 100 Mpc cube in a simulated mixed-dark-matter universe with 
0 = 1, showing the present-day structure that results from the growth of small density fluctuations in the very early universe. In this particular calculation, 20 percent of the total mass was assumed to be in the form of hot-dark-matter particles (actually, neutrinos); the rest was cold dark matter. Colors represent mass density, ranging from the cosmic mean (dark blue), through green, yellow, and red, to 100 times the mean (white). The enlargements zoom in on one particular galaxy in one particular small group of galaxies. The final frame (at bottom left) is roughly 1.5 Mpc across. Notice both the large-scale filamentary structure evident in the top two frames and the extensive dark-matter halos surrounding individual galaxies (the galaxies are roughly the white regions in the bottom two frames).
Because dark matter does not interact directly with photons, its density variations do not cause large (and easily observable) temperature variations in the microwave background. However, the radiation is influenced slightly by the gravity of the growing dark clumps, experiencing a slight gravitational redshift that varies from place to place depending on the dark-matter density. As a result, dark-matter models predict that there should be tiny "ripples" in the microwave background—temperature variations of only a few parts per million from place to place on the sky.
Until the late 1980s these ripples were too small to be accurately measured, although cosmologists were confident that they would be found. In 1992, after almost two years of careful observation, the COBE team (see Section 26.6) announced that the expected ripples had indeed been detected. The temperature variations are tiny—only 30—40 millionths of a kelvin from place to place in the sky—but they are there. The COBE results are displayed as a temperature map of the microwave sky in Figure 27.16(a). The temperature variation due to Earth's motion (see Figure 26.20) has been subtracted out, as has the radio emission from the Milky Way, and temperature deviations from the average are displayed.
Figure 27.16 (a) COBE map of temperature fluctuations in the cosmic microwave background. Hotter-than-average regions are shown in red, cooler-than-average regions in blue. The total temperature range shown is ±200 millionths of a kelvin. (b) Simulated map of microwave background temperature fluctuations corresponding to the simulation shown in Figure 27.15. Dark blue and red represent temperature variations of ±200 millionths of a kelvin from the average, so this map can be compared more or less directly with the COBE map in part (a). However, the resolution here is about 0.5 °—20 times sharper than the COBE map, and roughly the resolution expected in the next generation of satellite observations.
Initially, it seemed that the inhomogeneities in the microwave background were not consistent with the "standard" dark-matter models that provided the best agreement with actual observations of structure in the present-day universe. The ripples seen by COBE, taken in conjunction with the models, appeared to imply too little structure on large scales—that is, the computer simulations predicted fewer superclusters, voids, Great Walls, and so on, than are actually seen. However, with some modifications to the details of the models, it now looks as though the disagreement is not so serious as it first seemed, and a growing number of cosmologists are coming to regard the COBE observations as confirmation of a central prediction of dark-matter theory.
The simulation shown in Figure 27.15 implies temperature fluctuations in the microwave background that agree very well with the present COBE observations, but theorists can (of course) go one stage further. Figure 27.16(b) presents a prediction, based on the same simulation, of the temperature fluctuations that should be observed by the next generation of (much higher resolution) satellite experiments. If our current understanding of the microwave background anisotropy is correct, then future maps should look qualitatively like this one.
If the COBE results hold up—as they are checked and rechecked by collaborators and competitors alike—they may one day come to rank alongside the discovery of the microwave background itself in terms of their importance to the field of cosmology.
