Questions
Review Questions
What is the horizon problem? What is the flatness problem? How can these problems be resolved by the idea of inflation?The inflationary epoch lasted a mere 10−32 second. Why, then, is it worthy of so much attention by scientists?
In what ways is inflation similar to the present-day expansion of the universe? In what ways is it different?
Explain why the inflationary model does not violate the principle that the speed of light in a vacuum represents the ultimate speed limit.
Describe an example of each of the four basic types of interactions in the physical universe. Do you think it possible that a fifth force might be discovered someday? Explain your answer.
If gravity is intrinsically so weak compared to the strong force, why do we say that gravity rather than the strong force keeps the planets in orbit around the Sun? (Hint: Forces have a strength and a range.)
Explain how changes in the energy of the vacuum can account for the rapid expansion during the inflationary epoch.
What is the Heisenberg uncertainty principle? How does it lead to the idea that all space is filled with virtual particle-antiparticle pairs?
What is the difference between an electron and a positron?
What happens when an electron and a positron annihilate?
Is it possible for photons to create a particle pair of matter and antimatter? If so, what kind of photons?
Is it possible for a single hydrogen atom, with a positively charged proton and a negatively charged electron, to be created as a virtual pair? Why or why not?
Which can exist for a longer time, a virtual electron-positron pair or a virtual proton-antiproton pair? Explain your reasoning.
Explain why antimatter was present in copious amounts in the early universe but is very rare today.
What is meant by the threshold temperature of a particle?
Explain the connection between the fact that humans exist and the imbalance between matter and antimatter in the early universe.
Explain the connection between particles and antiparticles in the early universe and the cosmic microwave background that we observe today.
What is the deuterium bottleneck? Why was it important during the formation of nuclei in the early universe?
How does nucleosynthesis provide strong evidence for a hot big bang?
Why were only the four lightest chemical elements produced in the early universe?
The first stars in the universe are thought to have appeared some 400 million (4 × 108) years after the Big Bang. Once these stars formed, thermonuclear fusion reactions began in their interiors. Explain why these were the first fusion reactions to occur since the universe was 15 minutes old.
Why is it reasonable to suppose that all space is filled with a neutrino background analogous to the cosmic microwave background?
What is the Jeans length? Why is it significant for the formation of structure in the universe?
Why do astronomers suspect that globular clusters were among the first objects to form in the history of the universe? Why not something larger and more massive?
What are Population III stars? How do they differ from stars found in the present-day universe? Why are they so difficult to detect directly?
Describe the large-scale structure of the universe as revealed by the distribution of clusters and superclusters of galaxies.
What is the difference between hot and cold dark matter? How do astronomers decide which was more important in the formation of large-scale structures such as clusters of galaxies?
How did the presence of dark energy help to “turn off” the process of structure formation in the universe?
Describe the observational evidence, if any, for (a) the Big Bang, (b) the inflationary epoch, (c) the confinement of quarks, and (d) the era of recombination.
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Advanced Questions
Problem-solving tips and tools
We described Wien’s law for blackbody radiation in Section 5-4. If light with wavelength λ0 is emitted by an object at redshift z, the wavelength that we measure is λ = λ0 (1 + z). As explained in Section 26-6, the critical density ρc is equal to 3H02/8πG; that is, ρc is proportional to the square of the Hubble constant H0. If H0 = 73 km/s/Mpc, the critical density is equal to about 1.0 × 10−26 kg/m3. It is also useful to know that the mass of a proton is 1.67 × 10−27 kg, the mass of an electron is 9.11 × 10−31 kg, the mass of the Sun is 1.99 × 1030 kg, that 1 m3 = 106 cm3, that 1 light-year = 9.46 × 1015 m, and that 1 GeV = 103 MeV = 109 eV.
An electron has a lifetime of 1.0 × 10−8 seconds in a given energy state before it makes a transition to a lower state. What is the uncertainty in the energy of the photon emitted in this process?
How many times stronger than the weak force is the electromagnetic force? How many times stronger than the electromagnetic force is the strong force? Use this information to suggest one reason why the electromagnetic and weak forces can become unified at a lower energy than do the electroweak and strong forces.
How long can a proton-antiproton pair exist without violating the principle of the conservation of mass?
The mass of the intermediate vector boson W+ (and of its antiparticle, the W−) is 85.6 times the mass of the proton. The weak nuclear force involves the exchange of the W+ and the W−. (a) Find the rest energy of the W. Give your answer in GeV. (b) Find the threshold temperature for the W+ and W−. (c) From Figure 26-10, how long after the Big Bang did W+ and W− particles begin to disappear from the universe? Explain your answer.
Using the physical conditions present in the universe during the era of recombination (T = 3000 K and ρm = 10−18 kg/m3), show by calculation that the Jeans length for the universe at that time was about 100 ly and that the total mass contained in a sphere with this diameter was about 4 × 105 M⊙.
(a) If a Population III star had a surface temperature of 105 K, what was its wavelength of maximum emission? In what part of the electromagnetic spectrum does this wavelength lie? (b) To ionize a hydrogen atom requires a photon of wavelength 91.2 nm or shorter. Explain how Population III stars caused reionization. (c) If reionization occurred at z = 11, what do we measure the wavelength of maximum emission of a Population III star to be? In what part of the electromagnetic spectrum does this wavelength lie? (d) The image that opens this chapter was made using infrared wavelengths. Suggest why these wavelengths were chosen.
(a) If the Hubble constant is 73 km/s/Mpc, the critical density ρc is 1.0 × 10−26 kg/m3. The average density of dark matter is known to be about 0.20 times the critical density. Suppose that massive neutrinos constitute this dark matter, and the average density of neutrinos throughout space is 100 neutrinos per cubic centimeter. (In fact, the density of neutrinos is far less than this.) Under these assumptions, what must be the mass of the neutrino? Give your answers in kilograms and as a fraction of the mass of the electron. (b) Why do astronomers think that massive neutrinos are not the dominant type of dark matter in the universe?
A typical dark nebula (see Figure 18-4) has a temperature of 30 K and a density of about 10−12 kg/m3. (a) Calculate the Jeans length for such a dark nebula, assuming that the nebula is composed mostly of hydrogen. Express your answer in meters and in light-years. (b) A typical dark nebula is several light-years across. Is it likely that density fluctuations within such nebulae will grow with time? (c) Explain how your answer to (b) relates to the idea that protostars form within dark nebulae (see Section 18-3).
At the time labeled z = 4.97 in Figure 26-19, how large was the length of each side of the box used in the simulation compared to its size in the present day (z = 0)? How much greater was the density at z = 4.97 than the present-day density?
Discussion Questions
If you hold an iron rod next to a strong magnet, the rod will become magnetized; one end will be a north pole and the other a south pole. But if you heat the iron rod to 1043 K (770°C = 1418°F) or higher, it will lose its magnetization and there will be no preferred magnetic direction in the rod. This demagnetization is an example of restoring a spontaneously broken symmetry. Explain why.
Some GUTs predict that the proton is unstable, although with a half-life far longer than the present age of the universe. What would it be like to live at a time when protons were decaying in large numbers?
Web/eBook Questions
Search the World Wide Web for information about the top quark. What kind of particle is it? How does it compare with the up and down quarks found in protons and neutrons? Why did physicists work so hard to try to find it?
Search the World Wide Web for information about primordial deuterium (that is, deuterium that was formed in the very early universe). Why are astronomers interested in knowing how abundant primordial deuterium is in the universe? What techniques do they use to detect it?
Search the World Wide Web for information about the South Pole Telescope. What is the purpose of this telescope? Why is it sited at the South Pole? How will it help us understand the early universe?
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