At present, the density of matter in the universe greatly exceeds the equivalent mass density of radiation. The universe is matter dominated. The density of matter was much greater in the past, when the universe was smaller. However, because radiation is redshifted as the universe expands, the density of radiation was greater still. The early universe was radiation dominated. During the first few minutes after the Big Bang, matter was formed out of the primordial fireball by the process of pair production. In the early universe, matter and radiation were linked by this process. Particles "froze out" of the radiation background as the temperature fell below the threshold for creating them. The existence of matter today means that there must have been unequal amounts of matter and antimatter early on.
The physical state of the universe can be understood in terms of present-day physics back to about 10-43 s after the Big Bang. Before that, the four fundamental forces of nature—gravity, electromagnetism, the strong force, and the weak force—were all indistinguishable. There is presently no theory that can describe these extreme conditions. As the universe expanded and its temperature dropped, the forces became distinct from one another. First gravity, then the strong force, and then the weak and electromagnetic forces separated out.
Only a little of the helium observed in the universe today was formed in stars. Most of it was created by primordial nucleosynthesis in the early universe. Some deuterium was also formed at these early times, and it provides a sensitive indicator of the present density of the universe in the form of "normal" (as opposed to dark) matter. Studies of deuterium indicate that normal matter can account for at most 3 or 4 percent of the critical density. The remaining mass inferred from studies of clusters must then be made of dark matter, in the form of unknown particles formed at some very early epoch.
When the universe was about 1500 times smaller than it is today, the temperature became low enough for atoms to form. At that time, the (then-optical) radiation background decoupled from the matter. The universe became transparent. The photons that now make up the microwave background have been traveling freely through space ever since.
According to modern Grand Unified Theories, when the three nongravitational forces of nature began to display their separate characters, about 10-35 s after the Big Bang, a brief period of rapid cosmic expansion called the epoch of inflation occurred, during which the size of the universe increased by a factor of about 1050.
Cosmologists wonder why regions of the universe that have not had time to "communicate" with one another look so similar. This is called the horizon problem. Inflation solves it by taking a small homogeneous patch of the early universe and expanding it enormously in size. The patch is still homogeneous, but it is now much larger than the portion of the universe we can see today.
Cosmologists also wonder why the density of the universe seems to be so near the critical value. This is called the flatness problem. Inflation implies that the cosmic density is in fact exactly critical. If this is the case, then over 95 percent of the matter in the universe is dark.
The large-scale structure observed in the universe could not have formed out of density fluctuations in normal gaseous matter—there simply has not been enough time, given the twin constraints of the smoothness of the microwave background and the epoch at which the first galaxies and quasars are known to have formed. Instead, dark matter clumped and grew to form the "skeleton" of the structure now observed. Normal matter then flowed into the densest regions of space, eventually forming the galaxies we now see.
Cosmologists distinguish between hot dark matter and cold dark matter, depending on its temperature at the end of the Radiation Era. In order to explain the observed large-scale structure in the universe, much of the dark matter must be cold. In 1992 the COBE satellite discovered the expected ripples in the cosmic microwave background associated with the clumping of dark matter at early times.
1. The light emitted from all the stars in the universe now far outshines the cosmic microwave background. (Hint)
2. The time between the Big Bang and 10-43 afterward cannot be described for lack of a theory of quantum gravity. (Hint)
3. All elementary particle formation was completed by the time the universe was about 1 second old. (Hint)
4. About 25 percent by mass of matter in the universe is primordial helium. (Hint)
5. The present-day abundance of deuterium gives information on the density of normal matter. (Hint)
6. Decoupling refers to interactions between matter and antimatter. (Hint)
7. The present-day microwave background radiation originated just before the period of decoupling. (Hint)
8. After decoupling, neutral atoms could finally exist. (Hint)
9. The horizon problem relates to the isotropy of the microwave background radiation. (Hint)
10. The flatness problem is the fact that the observed density of matter is unexpectedly different from the critical density. (Hint)
11. Inflation was caused by the freeze-out of the strong force. (Hint)
12. The universe grew in size by a factor of about 10,000 during the inflationary period. (Hint)
13. If the theory of inflation is correct, then the density of the universe is exactly the critical density. (Hint)
14. Physicists have detected cold-dark-matter particles in terrestrial laboratories. (Hint)
15. Galaxies had already formed by the time the universe was about 1 million years old. (Hint)
1. Comparing the mass density of radiation and matter, we find that, at the present time, _____ dominates. (Hint)
2. Energetically speaking, radiation and matter were equally important approximately _____ years after the Big Bang. (Hint)
3. In the process of pair production, two _____ interact to form a particle and an _____. (Hint)
4. The temperature necessary to form electrons and positrons is about _____ K. (Hint)
5. The temperature necessary to form protons and _____ is about _____ K. (Hint)
6. When the universe was a few minutes old, nuclear fusion produced _____ and _____. (Hint)
7. After about a million years, _____ had formed in the universe. (Hint)
8. Elements heavier than helium were not formed primordially because, as time passed, the density and temperature of the universe _____. (Hint)
9. The fact that the density of normal matter is so much less than the known density of matter in the universe implies that much of the dark matter must be ____. (Hint)
10. The cosmic microwave background radiation last interacted with matter when the universe was about _____ times its present size. (Hint)
11. If the theory of inflation is correct, then dark matter must make up about _____ percent of all matter in the universe. (Hint)
12. Which had density fluctuations first, normal matter or dark matter? _____. (Hint)
13. We know that density fluctuations in the normal-matter component of the early universe must have been very small because otherwise we would see their imprint on the _____. (Hint)
14. Hot and cold dark matter differ in the masses of their particles. Cold dark matter consists of _____ particles. (Hint)
15. Theory predicted tiny fluctuations in the _____ of the microwave background; the _____ satellite found them. (Hint)
1. For how long was the universe dominated by radiation? How hot was the universe when the dominance of radiation ended? (Hint)
2. Why is our knowledge of the Planck epoch so limited? (Hint)
3. When and how did the first atoms form? (Hint)
4. Describe the universe at the end of the galactic epoch. (Hint)
5. Why do all stars, regardless of their abundance of heavy elements, seem to contain at least one-quarter helium by mass? (Hint)
6. Why didn't heavier and heavier elements form in the early universe, as they do in stars? (Hint)
7. If large amounts of deuterium formed in the early universe, why do we see so little deuterium today? (Hint)
8. How do measurements of the cosmic deuterium abundance provide a reliable estimate of 
0? (Hint)
9. When did the universe become transparent to radiation? (Hint)
10. What are GUTs? (Hint)
11. How does cosmic inflation solve the horizon problem? (Hint)
12. How does cosmic inflation solve the flatness problem? (Hint)
13. What is the difference between hot and cold dark matter? (Hint)
14. What is the connection between dark matter and the formation of large- and small-scale structures? (Hint)
15. Why were the observations made by the COBE satellite so important to cosmology? (Hint)
1. What was the equivalent mass density of the cosmic radiation field when the universe was one-thousandth its present size?(Hint)
2. Estimate the temperature needed for electron-positron pair production. The mass of an electron is 9.1 
10-31 kg. Use E = mc2 to find the energy (Section 16.5), E = hf to find the frequency f of a photon having that energy (Section 4.2), and finally Wien's law to find the temperature for which a blackbody spectrum peaks at that fequency (Section 3.4). How does your answer compare with the threshold temperature given in the text? (Hint)
3. Given that the threshold temperature for the production of electron—positron pairs is about 6 109 K and that a proton is 1800 times more massive than an electron, calculate the threshold temperature for proton—antiproton pairs. (Hint)
4. By what factor did the volume of the universe increase during the epoch of primordial nucleosynthesis, from the time when deuterium could first survive until the time at which all nuclear reactions ceased? By what factor did the matter density of the universe decrease during this period? (Hint)
5. From Table 25.1, the "photosphere" in the universe corresponding to the epoch of decoupling presently lies some 9000 Mpc from us (see Figure 27.7). How far away was the photosphere when the background radiation we see today was emitted? (Hint)
6. Calculate the mass, in kilograms, of the particle that unifies the strong and electroweak forces, if it froze out at a temperature of 1028 K. Calculate the mass of a hypothetical particle that might unify gravity with the other forces, given that it froze out at the end of the Planck epoch (Table 27.1). (Hint)
7. How many times did the universe double in size during the inflationary period if it expanded by a fact of 1050? (Hint)
8. What would be the radius of a million—solar mass patch of a homogeneous, critical-density universe (a) today? (b) At decoupling? (c) At the end of the nuclear epoch? (Hint)
9. The "blobs" evident in Figure 27.16(a) are about 10 ° across. If those blobs represent clumps of matter around the time of decoupling, and assuming Euclidean geometry, estimate the size of the clumps (at the time of decoupling). (Hint)
10. If dark-matter particles are remnants of the GUT era, they must have decoupled from the rest of the matter and radiation in the universe at the end of the GUT epoch. Repeat problem 5, but for dark-matter particles instead of electromagnetic photons, assuming a present photosphere distance of 9200 Mpc. (Hint)
1. Read the book The First Three Minutes, by Steven Weinberg. It is fairly nonmathematical in its presentation. What new results are presented in this chapter that were not known by Weinberg when he wrote the first edition of this book in 1977? How much progress has been made in understanding the very earliest epochs since that time?
2. Write a paper on the cosmological constant. It there presently any observational evidence favoring a nonzero value for this constant? What are the main theoretical reasons for including a cosmological constant in theories of the universe?
