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Chapter 26 - Cosmology
CHAPTER 26
COSMOLOGY
CHAPTER OUTLINE AND LECTURE NOTES
1. Hubble’s Law Revisited
Early editions of this book included a discussion of the steady-state theory. I removed it in
the third edition simply because of the rapidly growing amount of material on cosmology
that just had to be included. You might, however, want to consider adding a discussion of
the steady-state theory not because it is a credible theory of cosmology but because it shows
how scientists test cosmological models in particular and scientific models in particular.
One of the critical differences between science and other kinds of disciplines is that a good
scientific theory must make testable predictions. By this measure, the steady-state theory,
though wrong, was a very good theory.
2. Cosmological Models
I spend quite a bit of time in my lectures talking about the properties of one- and twodimensional flat and curved spaces in order to prepare the students for the attempt to
understand the important geometrical properties of three-dimensional spaces. Even though
they can’t visualize three-dimensional curved space, the students can extrapolate from oneand two-dimensional spaces (such as the surface of a chalk globe) to see that it would be
finite, unbounded, and would have no center.
3. The Big Bang
An interesting topic, closely related to the cosmic background radiation, is Olber’s paradox,
or the dark night sky paradox. This puzzle, which dates to at least the time of Halley in the
1700s, asks, “If the universe is infinite and stars are uniformly distributed then in any
direction our gaze should eventually reach a star. Why then, is the sky dark at night?”. As
Edward Harrison pointed out in his book Cosmology: The Science of the Universe, the
correct resolution to the paradox was given, amazingly, by Edgar Allen Poe in 1848. He
described the paradox and then wrote, “The only mode, therefore, in which, under such a
state of affairs, we could comprehend the voids which our telescopes find in innumerable
directions, would be by supposing the distance of the invisible background so immense that
no ray from it has yet been able to reach us at all.” In other words, in most directions we
would have to look so far to see a star that the light from that star hasn’t yet had time to
travel to us.
When we look out in space and back in time far enough to see the recombination epoch
we see an opaque bright universe in every direction. This is, of course, the cosmic
microwave background (CMB), shown in Figure 26.20.
4. Inflation
Early editions of this book discussed the cause of inflation in terms of a phase-change. This
was one of the possibilities being considered at the time of the first edition. I am grateful to
Dr. Andrei Linde, one of the leading cosmology theorists, who pointed out to me that
current ideas about the cause of inflation involve scalar fields rather than phase-change. Dr.
Linde also suggested some very helpful references.
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Chapter 26 - Cosmology
5. The Fate of the Universe
You might enjoy asking your students which of the two possibilities for the future of the
universe (continued expansion or eventual contraction) they prefer. My classes invariably
express a fairly strong preference for eventual contraction.
KEY TERMS
annihilation — The mutual destruction of a matter-antimatter pair of particles. The charges on
the two particles cancel and the mass of the particles is entirely converted to energy.
antimatter — The type of matter that annihilates ordinary matter on contact. For every particle
here is a corresponding antimatter particle. For example, the antimatter counterpart of the
proton is the antiproton.
Big Bang — The explosive event at the beginning of the universe. The expansion produced the
Big Bang that continues today.
cosmic microwave background radiation (CMB) — Radiation observed with almost perfectly
uniform brightness in all directions in the sky. The CMB is highly redshifted radiation
produced about a million years after the universe began to expand.
cosmological constant — A self-repelling property of space first proposed by Einstein.
cosmological principle — The assumption that all observers in the universe at a given time
would observe the universe to have the same essential features and large-scale structure.
cosmology — The study of the universe as a whole.
critical density — The value that the average density of the universe must equal or exceed if the
universe is closed. If the density of the universe is less than the critical density, the
universe will continue to expand forever.
dark energy – A form of energy that may be causing the expansion of the universe to accelerate.
decoupling epoch — The time about a million years after the expansion of the universe began
when the universe became transparent and light could, for the first time, travel great
distances before being absorbed or scattered. The cosmic background radiation was
produced at the decoupling epoch.
deuteron — A nucleus of deuterium, an isotope of hydrogen. A deuteron contains one proton
and one neutron.
Hubble time — An estimate of the age of the universe obtained by taking the inverse of
Hubble’s constant. The estimate is only valid if there has been no acceleration or
deceleration of the expansion of the universe.
inflation — A brief period of extremely rapid and enormous expansion that may have occurred
very early in the history of the universe.
isotropic — Looking the same in all directions.
pair production — A process in which a gamma ray is transformed into a particle and its
antiparticle (such as an electron and a positron).
radiation era — The period of time, before about 1 million years after the expansion of the
universe began, when radiation rather than matter was the dominant constituent of the
universe.
recombination epoch — The time, about 1 million years after the expansion of the universe
began, when most of the ions and electrons in the universe combined to form atoms.
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scalar field — A form of energy that has been proposed as the cause of inflation in the early
universe.
ANSWERS TO QUESTIONS AND PROBLEMS
Conceptual Questions
1. If the expansion has neither speeded up nor slowed down since the Big Bang
2. The expansion age would be cut in half.
3. 12 billion years.
4. No point on the surface of a ball is different from any other point.
5. Flat universes are infinite, positively curved universes are finite. Neither flat universes nor
positively curved universes have boundaries or centers.
6. The sum of the angles of large triangles could be measured and compared to see if they are
larger than 180°, in which case space is positively curved, or the ratios of circumference to
radius in large circles could be determined to see if they are less than 2, in which case
space is positively curved.
7. If the sum of the angles of large triangles is less than 180°, space is negatively curved. If it
is greater than 180°, space is positively curved. If the ratio of circumference to radius
increases with distance, space is negatively curved. If it decreases with increasing distance,
space is positively curved.
8. If the number of galaxies increases as r2, space is flat. If it increases less rapidly with
distance, space is positively curved. If it increases more rapidly, space is negatively curved.
9. If density is less than the critical density, space has negative curvature.
10. One
11. A large value of Hubble’s constant (rapid expansion) and low density
12. The larger the value, the shorter the actual age is compared to the expansion age.
13. They are fainter and more distant than expected if expansion were constant or slowing
down. This means that the present value of Hubble’s constant, which we use to estimate
distances, is greater than it has been in the past. Thus, expansion is accelerating.
14. He invented the cosmological constant to keep his cosmological models from predicting
either the expansion or contraction of the universe.
15. Dark energy would cause the expansion rate to increase with time.
16. The universe must be at least as old as the globular clusters it contains.
17. After 1 second the radiation in the universe lacked the energy to produce pairs of particles.
18. They were produced in annihilations of matter and anti-matter.
19. Before 100 seconds, energetic gamma rays disrupted deuterons as soon as they formed.
After 300 seconds, protons lacked sufficient energy to react to form deuterons.
20. It was quickly absorbed by surrounding matter.
21. To see the universe at the time the CMB was emitted, we need to look far back in time and
so far out in space that the radiation from those parts of the universe is redshifted from
visible light to radio radiation.
22. The spectrum and brightness of the CMB correspond to those of a blackbody with a
temperature of 2.74 K.
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23. They tell us that space is flat and that normal matter made up only a few percent of the
density of the universe at the time the CMB was emitted.
24. The region from which the CMB is seen was millions of light years wide at the time the
CMB was emitted when the universe was only a few hundred thousand years old. There
was no time for energy to flow from hot regions to cool ones to equalize the temperature
across the region so that the CMB could be so isotropic.
25. Because the departure from flatness has increased greatly since the Big Bang. This means
that the early universe must have been flat to one part in 1015.
26. During inflation the curvature of the universe was rapidly driven toward flatness.
27. It will eventually contract.
Problems
1. 14 billion years
2. 25 billion years
3. 49 km/s/Mpc
Figure-based Questions
1. Protons and neutrons at 100 s, protons and helium nuclei at 1000 s, fusion of hydrogen into
helium took place between those two times
2. About 10 -24 kg/m3, approximately 1000 to 10,000 times the actual density of the universe
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