On scales larger than a few hundred megaparsecs, the universe appears roughly homogeneous (the same everywhere) and isotropic (the same in all directions, ). In cosmology—the study of the universe as a whole—researchers usually simply assume that the universe is homogeneous and isotropic. This assumption is known as the cosmological principle. It implies that the universe cannot have a center or an edge.
If the universe were homogeneous, isotropic, infinite, and unchanging, then the night sky would be bright because any line of sight would eventually intercept a star. The fact that the night sky is dark is called Olbers's paradox. Its resolution lies in the fact that, regardless of whether or not the universe is infinite, we see only a finite part of it from Earth—the region from which light has had time to reach us since the universe began.
Tracing the observed motions of galaxies back in time implies that some 15 billion years ago, the universe consisted of a single point that then began to expand rapidly, at the time of the Big Bang. However, the galaxies are not simply flying apart into the rest of an otherwise empty universe. Space itself is expanding. The Big Bang did not happen at any particular location in space, because the entire universe was compressed to a point at that instant—the Big Bang happened everywhere at once. The cosmological redshift occurs as a photon's wavelength is "stretched" by cosmic expansion. The extent of the observed redshift is a direct measure of the expansion of the universe since the photon was emitted.
Although Einstein's theory of general relativity is needed for a full description of the cosmos, the dynamics of the universe can be understood using simple Newtonian concepts. The eventual fate of the universe depends on its density. If the density is greater than the critical density, then there is enough cosmic matter to stop the expansion and cause the universe to recollapse. If the density is less than the critical value, the universe will expand forever. Luminous matter by itself contributes only about 1 percent of the critical density. When dark matter in galaxies and clusters is taken into account, the figure rises to 20 or 30 percent. The fraction of dark matter on larger scales is uncertain, but it may be even greater than is found in clusters. Most astronomers believe that the present density lies somewhere between 10 and 100 percent of the critical value.
For H0 = 65 km/s/Mpc, the age of a critical-density universe is about 10 billion years. This age estimate may be in conflict with the ages of globular clusters derived from studies of stellar evolution. If the cluster ages are correct, then the density of the universe must be significantly less than critical, or Hubble's constant must be less than 65 km/s/Mpc.
General relativity provides a description of the geometry of the universe on the largest scales. The curvature of spacetime in a high-density universe is sufficiently large that the universe "bends back" on itself and is finite in extent, somewhat like the surface of a sphere. Such a universe is said to be a closed universe. A low-density open universe is infinite in extent and has a "saddle-shaped" geometry. The intermediate-density critical universe will expand forever, but it is spatially flat.
The cosmic microwave background is isotropic blackbody radiation that fills the entire universe. Its present temperature is about 3 K. The existence of the microwave background is direct evidence that the universe expanded from a hot, dense state. As the universe has expanded, the initially high energy radiation has been redshifted to lower and lower temperatures.
1. Cosmic homogeneity can be tested observationally, but cosmic isotropy has no observational test. (Hint)
2. Olbers's paradox asks, Why is the night sky dark?
3. Olbers's paradox is resolved by the cosmological redshift, which reduces the energy of photons received from very distant objects. (Hint)
4. Hubble's law implies that the universe will expand forever. (Hint)
5. The Big Bang is an expansion only of matter, not of space. (Hint)
6. All points in space appear to be at the center of the expanding universe. (Hint)
7. For H0 = 65 km/s/Mpc, a critical-density universe is approximately 10 billion years old. (Hint)
8. Cureent physics can describe the universe as far back in time as 1 second after the Big Bang, but no earlier. (Hint)
9. The cosmological redshift is a direct measure of the expansion of the universe. (Hint)
10. As it travels through space a photon's wavelength expands at the same rate as the universe is expanding. (Hint)
11. According to the standard Big Bang model of the cosmos, the universe has only two possible futures: either it will continue to expand forever, or it will someday stop expanding and start to contract. (Hint)
12. If the universe recollapses, it must rebound into a new expansion cycle similar to the present one. (Hint)
13. A bound universe will ultimately end in a "cold death."
14. An unbound universe is geometrically flat. (Hint)
15. The cosmic microwave background is the highly redshifted radiation of the early Big Bang.
1. Pencil-beam surveys suggest that the largest structures in space are no larger than about _____ Mpc in size.
2. Homogeneous means "the same _____." (Hint)
3. Isotropic means "the same in all _____." (Hint)
4. Together, the assumptions of cosmic homogeneity and isotropy are known as the _____. (Hint)
5. If the universe had an edge, this would violate the assumption of _____. (Hint)
6. If the universe had a center, this would violate the assumption of _____. (Hint)
7. A Hubble constant of 65 km/s/Mpc gives a maximum age for the universe of _____ billion years. (Hint)
8. _____ is slowing the expansion of the universe. (Hint)
9. The _____ of the universe determines whether the universe will expand forever. (Hint)
10. A _____ value for Hubble's constant yields an age for the universe incompatible with the ages of the oldest globular clusters. (Hint)
11. Luminous matter makes up about _____ percent of the critical density. (Hint)
12. By observing distant galaxies, astronomers have determined that the universe was expanding _____ long ago than it is today. (Hint)
13. The surface of a sphere is a two-dimensional example of a _____ curved universe. (Hint)
14. An open universe has a density _____ the critical value. (Hint)
15. The temperature of the universe, as measured by the cosmic microwave background, is _____ K. (Hint)
1. What evidence do we have that there is no structure in the universe on very large scales? How large is "very large"? (Hint)
2. What is the cosmological principle? (Hint)
3. What is Olbers's paradox? How is it resolved? (Hint)
4. Explain how an accurate measure of Hubble's constant can lead to an estimate of the age of the universe. (Hint)
5. We appear to be at the center of the Hubble flow. Why doesn't this violate the cosmological principle? (Hint)
6. Why isn't it correct to say that the expansion of the universe involves galaxies flying outward into empty space? (Hint)
7. Where did the Big Bang occur? (Hint)
8. How does the cosmological redshift relate to the expansion of the universe? (Hint)
9. What measureable property of the universe determines whether or not it will expand forever? (Hint)
10. Is there enough luminous matter to halt the current cosmic expansion? (Hint)
11. Is there enough dark matter to halt the current cosmic expansion? (Hint)
12. What is the significance of cosmic microwave background? (Hint)
13. Why does the temperature of the microwave background fall as the universe expands? (Hint)
14. Many cultures throughout history have developed their own cosmologies. Do you think the modern scientific cosmology is more likely to endure than any other? Why or why not?
15. Even with the recent revision of the value of Hubble's constant, estimates of the age of the universe based on H0 are still somewhat lower than estimates of the ages of many globular clusters in our own Galaxy (Interlude 26-2). How do you think astronomers should proceed in resolving this discrepancy?
1. What is the greatest distance at which a galaxy survey sensitive to objects as faint as 20th magnitude could detect a galaxy as bright as to the Milky Way (absolute magnitude -20)? (Hint)
2. If the entire universe were filled with Milky Way—like galaxies, with an average density of 1 per cubic megaparsec, calculate the total number of galaxies observable by the survey in the previous question, if it covered the entire sky.
3. Eight galaxies are located at the corners of a cube. The present distance from each galaxy to its nearest neighbor is 10 Mpc, and the entire cube is expanding according to Hubble's law, with H0 = 65 km/s/Mpc. Calculate the recession velocity of one corner of the cube relative to the opposite corner.
4. According to the Big Bang theory described in this chapter, what is the maximum possible age of the universe if H0 = 50 km/s/Mpc? 65 km/s/Mpc? 80 km/s/Mpc? (Hint)
5. For a Hubble constant of 65 km/s/Mpc, the critical density is 8 × 10-27kg/m3. (a) How much mass does that correspond to within a volume of 1 cubic astronomical unit? (b) How large a cube would be required to enclose 1 Earth mass of material? (Hint)
6. The Virgo Cluster is observed to have a recessional velocity of 1200 km/s. Assuming H0 = 65 km/s/Mpc and a critical-density universe, calculate the total mass contained within a sphere centered on Virgo and just enclosing the Milky Way Galaxy. What is the escape speed from the surface of this sphere? (Hint)
7. Assuming critical density, and using the distances presented in Table 25.1, estimate the total amount of matter in the observable universe. Express your answer (a) in kilograms, (b) in solar masses, and (c) in "galaxies," where 1 galaxy = 1011 solar masses.
8. The critical density is proportional to the square of Hubble's constant. If the critical density were equal to the known density of "normal" matter (not dark matter), about 10-28 kg/m3, what would be the corresponding value of Hubble's constant? Is this within the currently accepted range of values? (Hint)
9. What was the temperature of the cosmic microwave background at the epoch of quasar formation (at a redshift of 5)? (Hint)
10. Using the information given in problem 6, calculate the distance from our location to the point that would one day become the center of the Virgo Cluster, at the time when the temperature of the microwave background was equal to the present surface temperature of the Sun. (Hint)
1. Make a model of a two-dimensional universe and examine Hubble's law on it. Find a balloon that will expand into a nice large sphere. Blow it up about halfway and mark dots all over its surface; the dots will represent galaxies. Choose one dot as your home galaxy. Using a measuring tape, measure the distances to various other galaxies, numbering the dots so you will not confuse them later. Now blow the balloon up to full size and measure the distances again, and find the new distances to each dot. Calculate the change in the distances for each galaxy; this is a measure of their velocity (change in position/change in time; the time is the same for all and is arbitrary). Plot their velocities versus their new distances as in Figure 26.11. Do you get a straight-line correlation, i.e. a "Hubble" law? Does it matter which dot you choose as home? Demonstrate this to your class.
2. Write a paper on the philosophical differences between living in an open, closed, or flat universe. Are there aspects of any of these three possibilities that are hard to accept? It is quite possible that astronomers may determine within your lifetime which is correct. Do you have a preference?
3. Go to your library and read about the steady-state universe, which enjoyed some measure of popularity in the 1950s and 1960s. How does it differ from the standard Big Bang model? Why do you think the steady-state model is not widely accepted today—
