Questions

Review Questions

  1. Why did Isaac Newton conclude that the universe was static? Was he correct?

  2. What is Olbers’s paradox? How can it be resolved?

  3. What is a cosmological constant? Why did Einstein introduce it into cosmology?

  1. What does it mean when astronomers say that we live in an expanding universe? What is actually expanding?

  2. Describe how the expansion of the universe explains Hubble’s law.

  1. Would it be correct to say that due to the expansion of the universe, Earth is larger today than it was 4.56 billion years ago? Why or why not?

  2. Using a diagram, explain why the expansion of the universe as seen from a distant galaxy would look the same as seen from our Galaxy.

  3. How does modern cosmology preclude the possibility of either a center or an edge to the known universe?

  4. Explain the difference between a Doppler shift and a cosmological redshift.

  5. Explain how redshift can be used as a measure of lookback time. In what ways is it superior to time measured in years?

  6. By what factor has the universe expanded since z = 1? Explain your reasoning.

  7. What does it mean to say that the universe is homogeneous? That it is isotropic?

  8. What is the cosmological principle? How is it justified?

  9. How was the Big Bang different from an ordinary explosion? Where in the universe did it occur?

  10. Some people refer to the Hubble constant as “the Hubble variable.” In what sense is this justified?

  11. What is meant by “the observable universe”?

  12. (a) Explain why the radius of the observable universe is continually increasing. (b) Although the universe is 13.7 billion years old, the observable universe includes objects that are more than 13.7 billion light-years away from Earth. Explain why.

  13. Imagine an astronomer living in a galaxy a billion light-years away. Is the observable universe for that astronomer the same as for an astronomer on Earth? Why or why not?

  1. How did the abundance of helium in the universe suggest the existence of the cosmic background radiation?

  2. Can you see the cosmic background radiation with the naked eye? With a visible-light telescope? Explain why or why not.

  3. If the universe continues to expand forever, what will eventually become of the cosmic background radiation?

  1. How can astronomers measure the average mass density of the universe?

  2. What does it mean to say that the universe was once radiation-dominated? What happened when the universe changed from being radiation-dominated to being matter-dominated? When did this happen?

  3. What was the era of recombination? What significant events occurred in the universe during this era? Was the universe matter-dominated or radiation-dominated during this era?

  4. (a) Was there ever an era when the universe was radiation-dominated and matter and radiation were at the same temperature? If so, approximately when was this, and were there atoms during that era? If not, explain why not. (b) Was there ever an era when the universe was radiation-dominated and matter and radiation were not at the same temperature? If so, approximately when was this, and were there atoms during that era? If not, explain why not.

  5. Describe two different ways in which the cosmic microwave background is not isotropic.

  6. What is meant by the critical density of the universe? Why is this quantity important to cosmologists?

  7. Describe how astronomers use the cosmic background radiation to determine the geometry of the universe.

  8. Explain why it is important to measure how the expansion rate of the universe has changed over time. How is this rate measured?

  9. What is dark energy? Describe two ways that we can infer its presence.

  10. What does it mean to say that the universe is dark energy–dominated? What happened when the universe changed from being matter-dominated to being dark-energy–dominated?

  11. How can we detect the presence of sound waves in the early universe? What do these sound waves tell us?

Advanced Questions

Problem-solving tips and tools

We discussed Wien’s law in Section 5-4. You may find it useful to recall that 1 parsec equals 3.26 light-years, that 1 Mpc equals 3.09 × 1019 km, and that a year contains 3.16 × 107 seconds.

  1. (a) For what value of the redshift z were representative distances between galaxies only 20% as large as they are now? (b) Compared to representative distances between galaxies in the present-day universe, how large were such distances at z = 8? Compared to the density of matter in the present-day universe, what was the density of matter at z = 8? (c) If dark energy is in the form of a cosmological constant, how does its present-day density compare to the density of dark energy at z = 2? At z = 5? Explain your answers.

  2. The host galaxy of the supernova HST04Sas (see the image that opens this chapter) has a redshift z = 1.390. The light from this galaxy includes the Lyman-alpha (Lα) spectral line of hydrogen, with an unshifted wavelength of 121.6 nm. Calculate the wavelength at which we detect the Lyman-alpha photons from this galaxy. In what part of the electromagnetic spectrum does this wavelength lie?

  3. Estimate the age of the universe for a Hubble constant of (a) 50 km/s/Mpc, (b) 75 km/s/Mpc, and (c) 100 km/s/Mpc. On the basis of your answers, explain how the ages of globular clusters could be used to place a limit on the maximum value of the Hubble constant.

  4. Some people claim that the universe came into being about 6000 years ago. Find the value of the Hubble constant for such a universe. Is this a reasonable value for H0? Explain your answer.

  5. The quasar HS 1946+7658 has a redshift z = 3.02. At the time when the light we see from HS 1946+7658 left the quasar, how many times more dense was the matter in the universe than it is today?

  6. Use Wien’s law (Section 5-4) to calculate the wavelength at which the cosmic microwave background (T = 2.725 K) is most intense.

  7. If the mass density of radiation in the universe were 625 times larger than it is now, what would the background temperature be?

  8. Suppose that the present-day temperature of the cosmic background radiation were somehow increased by a factor of 100, from 2.725 K to 272.5 K. (a) Calculate ρrad in this situation. (b) If the average density of matter (ρm) remained unchanged, would it be more accurate to describe our universe as matter-dominated or radiation-dominated? Explain your answer.

  9. Calculate the mass density of radiation (ρrad) in each of the following situations, and explain whether each situation is matter-dominated or radiation-dominated: (a) the photosphere of the Sun (T = 5800 K, ρm = 3 × 10−4 kg/m3); (b) the center of the Sun (T = 1.55 × 107 K, ρm = 1.6 × 105 kg/m3); (c) the solar corona (T = 2 × 106 K, ρm = 5 × 10−13 kg/m3).

  10. If a photon from the cosmic microwave background had wavelength λ0 when it was emitted at redshift z, its wavelength today is λ = λ0(1 + z). (a) Let T be the symbol for the temperature of the cosmic microwave background today. Explain why the radiation temperature was T0 = T (1 + z) at redshift z. (b) What was the radiation temperature at z = 1? (c) At what redshift was the radiation temperature equal to 293 K (a typical room temperature)?

  11. What would be the critical density of matter in the universe (ρc) if the value of the Hubble constant were (a) 50 km/s/Mpc? (b) 100 km/s/Mpc?

  12. Consider the quasar HS 1946+7658 (see Advanced Question 37), which has z = 3.02. (a) Suppose that in the present-day universe, two clusters of galaxies are 500 Mpc apart. At the time that the light was emitted from HS 1946+7658 to produce an image on Earth tonight, how far apart were those two clusters? (b) What was the average density of matter (ρm) at that time? Assume that in today’s universe, ρm = 2.4 × 10−27 kg/m3. (c) What were the temperatures of the cosmic background radiation and the mass density of radiation (ρrad) at that time? (d) At this time in the remote past, was the universe matter-dominated, radiation-dominated, or dark-energy–dominated? Explain your answer.

  13. Whether the expansion of the universe is speeding up or slowing down, it can be expressed in terms of a quantity called the deceleration parameter, denoted by q0. The expansion is slowing down if q0 is positive and speeding up if q0 is negative; if q0 = 0, the expansion proceeds at a constant rate. If we assume that the dark energy is due to a cosmological constant, the deceleration parameter can be calculated using the formula
    (Recall that the density parameter 0 is equal to m + Λ.) (a) Show that if there is no cosmological constant, the expansion of the universe must slow down. (b) Using the values of m and Λ given in Table 25-2, find the value of the deceleration parameter for our present-day universe. Based on this, is the expansion of the universe speeding up or slowing down? (c) Imagine a universe that has the same value of m as our universe but in which the expansion of the universe is neither speeding up nor slowing down. What would be the value of Λ in such a universe? Which would be dominant in such a universe, matter or dark energy? Explain your answer.

  14. In general, the deceleration parameter (see Advanced Question 45) is not constant but varies with time. For a flat universe, the deceleration parameter at a redshift z is given by the formula
    where Λ is the dark energy density parameter. Using the value of Λ given in Table 25-2, find the value of qz for (a) z = 0.5 and (b) z = 1.0. (c) Explain how your results show that the expansion of the universe was actually decelerating at z = 1.0, but changed from deceleration to acceleration between z = 1.0 and z = 0.5.

  15. The dark energy density parameter Λ is related to the value of the cosmological constant Λ by the formula
    where c = 3.00 × 108 m/s is the speed of light. Determine the value of Λ if Λ and H0 have the values given in Table 25-2. (Hint: You will need to convert units to eliminate kilometers and megaparsecs.)

Discussion Questions

  1. Suppose we were living in a radiation-dominated universe. Discuss how such a universe would be different from the universe we now observe.

  2. How can astronomers be certain that the cosmic microwave background fills the entire cosmos, not just the vicinity of Earth?

  3. Do you think there can be “other universes,” regions of space and time that are not connected to our universe? Should astronomers be concerned with such possibilities? Why or why not?

Web/eBook Questions

  1. Before the discovery of the cosmic microwave background, it seemed possible that we might be living in a “steady-state universe” with overall properties that do not change with time. The steady-state model, like the Big Bang model, assumes an expanding universe, but it does not assume a “creation event” such as the Big Bang. Instead, matter is assumed to be created continuously everywhere in space to ensure that the average density of the universe remains constant. Search the World Wide Web for information about the steady-state theory. Explain why the existence of the cosmic microwave background was a fatal blow to the steady-state theory.

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