pattern which enhances perturbations of a certain wavelength. This preferred wavelength fits 220 times around the circumference of the sky. This preferred spot size can be seen in Figure 1.5 (use the app at http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe).
The acoustic scale can also be seen in the spatial distribution of galaxies. Galaxies are likely to form where the density is high, and for a given initial density peak that leads to a central spike of galaxies surrounded by a spherical shell of galaxies where the traveling sound wave ended up 400,000 years after the Big Bang. This separation can be measured by studying the correlation of galaxies: there is an enhanced probability that two galaxies are separated by 142 Mpc instead of 132 or 152 Mpc. This excess probability of galaxy separations of 142 Mpc is clearly seen in the data on galaxy clustering shown in Figure 1.6. The vertical scale shows the observed strength of clustering. Size scale increases along the horizontal axis. For the current value of the Hubble Constant, h = H0/100 = 0.7, the red arrow shows the increased clustering at a separation of 142 Mpc.
Figure 1.5. Picture of the CMB sky seen by the ESA Planck mission.
Figure 1.6. Strength of galaxy/galaxy clustering is shown on the vertical axis, versus separation, s, on the horizontal axis. The blue points are from the galaxy survey by Blake et al. (2011); the black points are from Eisenstein et al. (2005). The red arrow shows the excess probability of galaxy clustering on a separation scale of s = 142 Mpc, as predicted from sound waves crossing the Universe in its first 400,000 years.
Current Research
Dark Matter
The small density fluctuations indicated by the small temperature differences seen by COBE can grow into the galaxies and clusters of galaxies that we see in the Universe today, but only if the action of gravity is not impeded by other interactions. The most important epoch for the growth of structures is the period just after 50,000 years after the Big Bang. At this point, the density of matter becomes larger than the density of the background radiation, which allows dense regions to collapse under the influence of their own gravity. The temperature differences measured by COBE are a direct indication of the gravitational potential differences, which are equivalent to the heights and depths of mountains and valleys on Earth. In fact, a typical gravitational potential difference corresponds to ±300 million km in a constant gravitational acceleration equal to Earth’s surface gravity. But the distance between peaks and valleys in the Universe is astronomical: 300 quadrillion km. Thus, the gradient is very gentle, and only matter that moves freely downslope will be able to gather together in pools in the valleys. All chemical elements are ionized at the temperature of 30,000 K that existed 10,000 years after the Big Bang, and the resulting free electrons interact with the background radiation to produce a very strong interaction that resists the force of gravity. Thus, all ordinary matter acts like molasses and does not flow freely down the small gravitational gradients in the Universe. Therefore, most of the mass of the Universe must be made of exotic material that does not interact with radiation. It cannot scatter light, absorb light, or emit light. This is nonbaryonic dark matter. The nature of this dark matter is still quite uncertain.
Historically, the first candidate for nonbaryonic dark matter was the neutrino. Neutrinos are known to exist, and their number density, determined by the reactions in Equation (9), is fixed by the observed microwave background. If one of the three kinds of neutrino had a mass about 10,000 times smaller than the mass of the electron, the density of neutrinos in the Universe would be sufficient to give Ω = 1. But neutrinos with this tiny mass would have a speed of about 200,000 km/s at the critical time 10,000 years after the Big Bang. Because of this rapid motion, neutrinos are called hot dark matter. They would thus move about 7000 light years before slowing down as the Universe expanded. The 7000 light years would increase to 70 million light years now. In any dense region smaller than this, the neutrinos would escape before the dense region could collapse, so neutrino dark matter would produce only a very large-scale structure. Our observed Universe, to the contrary, contains ample smaller-scale structures such as galaxy clusters and super-clusters, which rule out neutrinos as the principal dark matter. The simulations in Figure 1.7 show that the many small dense structures which are predicted in a CDM universe (left), are erased in a hot dark matter universe (right).
Another model for nonbaryonic dark matter assumes the existence of a new, heavy, electrically neutral, and stable particle. This particle would interact very weakly with ordinary matter and radiation, so it received the name Weakly Interacting Massive Particle (WIMP). Because such a heavy particle would be moving very slowly 10,000 years after the Big Bang, WIMPs are a form of cold dark matter. One possible candidate for the dark matter is the neutralino, which is the lightest supersymmetric particle. Supersymmetric grand unified theories (Susy GUTs) are a currently favored class of models for the high energy particle interactions observed in particle accelerators. However, the cosmological predictions of the cold dark matter model do not depend on the nature of the cold dark matter particle. So even lacking the details, we can have some confidence in the accuracy of our general ideas about how the universe evolved, from an almost perfectly smooth state seen in the CMB at 400,000 years after the Big Bang, to the very highly structured Universe we see today.
Figure 1.7. Comparison of simulations of large-scale structures formed by cold dark matter (left) and hot dark matter (right). The many small dense structures (faint yellow points) evident in a CDM Universe are smeared away by streaming in a hot dark matter-dominated Universe (such as one in which the dark matter is neutrinos). Source: Maccio et al. (2012).
Dark Energy
The discovery that the expansion of the Universe is accelerating (see Alex Filippenko's Chapter 4 discussion of Type Ia supernovae distances) has led to the introduction of “dark energy” to the standard cosmological model. This could be a cosmological constant as introduced by Einstein, but it could also be a vacuum energy density, like the large vacuum energy during inflation. All the data collected to date are consistent with a constant vacuum energy density, but since the large vacuum energy during inflation went away, showing that dark energy changes are possible, many scientists are trying to measure the changes in the dark energy density. Studying the dark energy density as a function of time will be a primary science goal of the ESA Euclid mission and the NASA Wide Field Infrared Survey Telescope (WFIRST) mission.
Standard Model of Cosmology
The data described in this chapter have converted cosmology from a speculative metaphysical exercise into a data-driven branch of astrophysics. Detailed calculations have been done using a standard cosmological model that has the following components: a primordial perturbation spectrum that is very close to equal power on all scales as predicted by inflation, a flat geometry or a total density equal to the critical density as predicted by inflation, and three main densities. These are ordinary matter (all the atoms in the Universe) with density 0.4189 ± 0.0026 10−24 gram/ meter3, cold dark matter with density 2.232 ± 0.019 10−24 gram/meter3, and dark energy dominating with density 3349 ± 67 eV/centimeter3. (When expressed in directly comparable units, the dark energy density is a bit more