21st Century Astronomy

Laura Kay, Stacy Palen, Brad Smith

Chapter 22

Modern cosmology - all with Video Answers

Educators

Chapter Questions

Problem 1

The force that acts to slow the expansion of the universe is the ______ force.
a. gravitational
b. electromagnetic
c. strong nuclear
d. weak nuclear

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Problem 2

In an open universe, the angles of a triangle add to ______ $180^{\circ}$ and the circumference of a circle is ______ $2 \pi r$.

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Problem 3

If astronomers ignored any cosmological constant, the future of the universe could be determined solely from
a. the mass of the universe.
b. the volume of the universe.
c. the amount of light in the universe.
d. the density of the universe.

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Problem 4

The cosmological constant accounts for the effects of
a. dark matter.
b. the Big Bang.
c. dark energy.
d. gravity.

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Problem 5

The universe is accelerating. Therefore, the age of the universe is probably ______ than previously thought.

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Problem 6

The cosmic microwave background radiation indicates that the early universe
a. was quite uniform.
b. varied greatly in density from one place to another.
c. varied greatly in temperature from one place to another.
d. was shaped differently from the modern universe.

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Problem 7

Identify the two problems of cosmology that are solved by inflation.

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Problem 8

According to the definitions in Chapter 1 , superstring theory is
a. a hypothesis.
b. an idea.
c. a theory.
d. a law.
e. a principle.

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Problem 9

Place in order the following events in the history of the universe.
a. Planck era
b. grand unified theory breaks
c. today
d. Big Bang nucleosynthesis
e. electroweak breaks
f. theory of everything breaks
g. electron-positron pair annihilation
h. formation of galaxies and stars
i. recombination
j. inflation

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Problem 10

Place the following forces in order of their separation in the first moments after the Big Bang.
a. gravity
b. strong nuclear force
c. weak nuclear force
d. electromagnetic force

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Problem 11

True/False
$\mathbf{T} / \mathbf{F}:$ The sum of the angles of a triangle is always $180^{\circ}$

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Problem 12

True/False
T/F: Gravity acts to accelerate the universe.

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Problem 13

True/False
T/F: The future of the universe is determined only by the mass it contains.

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Problem 14

True/False
T/F: The light in the cosmic microwave background radiation is the oldest light in the universe.

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Problem 15

True/False
T/F: Grand unified theories combine all four fundamental forces in the universe.

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Problem 16

As applied to the universe, what is the meaning of critical density?
a. Above this density, nebulae collapse to form stars.
b. Above this density, dark matter becomes important.
c. Above this density, the universe will eventually collapse.
d. Above this density, matter becomes degenerate.

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Problem 17

Of the four fundamental forces in nature, which one depends on electric charge?
a. gravitational force
b. electromagnetic force
c. strong nuclear force
d. weak nuclear force

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Problem 18

The principal difference between normal matter and dark matter is that
a. normal matter interacts with light, while dark matter does not.
b. normal matter has gravity, while dark matter does not.
c. things made of normal matter are larger when they are more massive; things made of dark matter are smaller.
d. there is no difference; dark matter was just discovered later.

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Problem 19

Suppose you measure the angles of a triangle and find that they add to $185^{\circ} .$ From this you can determine that the space the triangle occupies is
a. flat.
b. positively curved.
c. negatively curved.
d. filled with dark matter.

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Problem 20

Quarks are
a. virtual particles.
b. massless particles.
c. candidates for dark matter.
d. building blocks of larger particles.

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Problem 21

Current understanding indicates that the universe is
a. closed.
b. flat.
c. open.
d. inflating.

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Problem 22

When a particle and an antiparticle come together, they
a. annihilate each other, releasing photons.
b. create a black hole.
c. release astronomical amounts of energy.
d. create new particles.

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Problem 23

The vast majority of antimatter in the early universe
a. is still around today, filling the space between galaxies.
b. became dark matter.
c. formed antimatter galaxies and stars.
d. annihilated with matter.

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Problem 24

Astronomers will never directly observe the first few minutes of the universe, because
a. the universe was opaque at that time.
b. the universe is too large now.
c. there were no particles or other matter to see.
d. there were no photons.

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Problem 25

The anthropic principle states that
a. the universe was created so that life exists.
b. life exists, so the universe must be such that life can exist.
c. if the universe were otherwise, life would not exist.
d. life has made the universe the way it is.

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Problem 26

What set of circumstances would cause an expanding universe to reverse its expansion and end up in a "Big Crunch"?

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Problem 27

Describe the observational evidence suggesting that Einstein's cosmological constant (a repulsive force) may be needed to explain the historical expansion of the universe.

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Problem 28

What do astronomers mean by dark energy?

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Problem 29

If the universe is being forced apart by dark energy, why isn't the Milky Way Galaxy, the Solar System, or the planet Earth being torn apart?

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Problem 30

Describe the cause and consequences of a Big Rip.

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Problem 31

In Chapter 19 we said we could estimate the age of the universe with Hubble time $\left(1 / H_{\mathrm{o}}\right) .$ Why does that method not give the best answer?

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Problem 32

What is the flatness problem, and why has it created difficulties for cosmologists?

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Problem 33

During the period of inflation, the universe may have briefly expanded at $10^{30}$ (a million trillion trillion) or more times the speed of light. Why did this ultra-rapid expansion not violate Einstein's special theory of relativity, which says that neither matter nor communication can travel faster than the speed of light?

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Problem 34

Why is particle physics important for understanding the early universe?

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Problem 35

The fundamental forces of the universe are generally assumed not to change.
a. How would the fate of the universe be affected if Newton's gravitational constant changed with time?
b. What if, instead, the electric force between charged particles changed with time?

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Problem 36

The standard model cannot explain why neutrinos have mass, or why electron-positron asymmetry existed in the early universe. Do these failings make it an incomplete theory? Should all of its predictions be ignored until the theory can resolve these remaining issues?

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Problem 37

Explain the process of pair production.

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Problem 38

Describe the Planck era.

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Problem 39

What are the basic differences between a grand unified theory (GUT) and a theory of everything (TOE)?

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Problem 40

Consider the term superstring theory in light of the discussion in Chapter 1. Many scientists object to using the word theory to describe superstring theory. Why?

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Problem 41

Study Figure 22.2
a. Is the vertical axis linear or logarithmic?
b. There are two labels for the horizontal axis. The top label is measured in billions of years. Is this axis linear or logarithmic?
c. The bottom label for the horizontal axis is measured in relative brightness. Is this axis linear or logarithmic?
d. What is the relationship between billions of years and relative brightness?

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Problem 42

Figure 22.2 shows a blue curve that indicates a model in which the universe first decelerated and then accelerated, as well as a red curve indicating continuous deceleration.
a. How are the two curves different?
b. What is it about one of these curves that indicates deceleration? What indicates acceleration?
c. If a straight line were plotted on this graph, what would the model that the new line represents indicate about the expansion of the universe?

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Problem 43

Study Figure $22.2 .$ On this graph, the colored lines represent various models, and the black dots represent data taken in the actual universe.
a. Why are there no data points on the right-hand side of the graph?
b. Which models are excluded by the data?
c. Roughly how far back in time do the data go?
d. What fraction of the age of the universe is the answer to part
(c) (assuming an age of 13.7 billion years)?

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Problem 44

Compare Figure $22.3,$ which shows several predictions for the future of possible universes and Figure $22.5,$ which displays data taken about our own universe. Given the data in Figure $22.5,$ which lines in Figure 22.3 must be rejected as possibilities for describing the future of the universe?

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Problem 45

Study Figure $22.5 .$ From the plotted data, determine the following:
a. Is the universe flat, open, or closed?
b. Will the universe expand forever, coast to a stop, or recollapse eventually?
c. Was there a Big Bang?
d. What is the most probable value of omega sub lambda $\left(\Omega_{N}\right) ?$ Of omega sub mass $\left(\Omega_{\operatorname{mas}}\right) ?$

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Problem 46

Suppose that new data coming in from a new instrument give the value 0.1 for both $\Omega_{\text {A }}$ and $\Omega_{\text {mass }} .$ How would astronomers probably respond to these new data?

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Problem 47

Study Figure 22.15
a. Is the time axis (the vertical dimension of the figure) approximately linear or approximately logarithmic?
b. By how many orders of magnitude (factors of 10 ) has the density $\rho$ of the universe dropped since earliest time?
c. By how many orders of magnitude has the temperature dropped since earliest time?

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Problem 48

Currently, the Hubble constant has an uncertainty of about 4 percent. What are the corresponding maximum and minimum ages allowed for the universe?

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Problem 49

How many hydrogen atoms need to be in 1 cubic meter $\left(\mathrm{m}^{3}\right)$ of space to equal the critical density of the universe?

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Problem 50

The universe today has an average density $\rho_{0}=3 \times 10^{-28} \mathrm{kg} / \mathrm{m}^{3}$ Assuming that the average density depends on the scale factor, as $\rho=\rho_{0} / R_{\mathrm{U}}^{3},$ what was the scale factor of the universe when its average density was about the same as Earth's atmosphere at sea level $\left(\rho=1.23 \mathrm{kg} / \mathrm{m}^{3}\right) ?$

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Problem 51

The proton and antiproton each have the same mass, $m_{n}=$ $1.67 \times 10^{-27} \mathrm{kg} .$ What is the energy (in joules) of each of the two gamma rays created in a proton-antiproton annihilation?

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Problem 52

There are about 500 million CMB photons in the universe for every hydrogen atom. What is the equivalent mass of these photons? Is it large enough to factor into the overall density of the universe?

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Problem 53

Suppose you brought together a gram of ordinary-matter hydrogen atoms (each composed of a proton and an electron) and a gram of antimatter hydrogen atoms (each composed of an antiproton and a positron). Keeping in mind that 2 grams is less than the mass of a dime,
a. Calculate how much energy (in joules) would be released as the ordinary-matter and antimatter hydrogen atoms annihilated one another.
b. Compare this amount of energy with the energy released by a 1-megaton hydrogen bomb $\left(1.6 \times 10^{14} \mathrm{J}\right)$

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Problem 54

One GUT theory predicts that a proton will decay in about $10^{31}$ years, which means if you have $10^{\text {si }}$ protons, you should see one decay per year. The Super-Kamiokande observatory in Japan holds about 20 million kg of water in its main detector, and it did not see any decays in 5 years of continuous operation. What limit does this observation place on proton decay and on the GUT theory described here?

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Problem 55

Assume a planet's orbit is perfectly circular as it travels in the gravitational well of its star. If this were true, would the orbit's circumference be greater than, less than, or equal to $2 \pi$ times the radius of the orbit?

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Problem 56

Animations of the stages after the Big Bang shown in Figure 22.15 can be found at these websites: http://expositions. bnf.fr/ciel/elf/1big/big.htm (ignore the text in French) and http://superstringtheory.com/cosmo/cosmo3.html. What are the major stages? What is the evidence for each of these stages?

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Problem 57

Go to the website for the Dark Energy Survey, an international project beginning in 2012 (https: $/ /$ www.darkenergysurvey org/index.shtml). What observations will be made for this project? What will it tell scientists about dark energy? Click on "News." What is the status of this project? Are there any results yet?

Robert Hackett

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Problem 58

Go to the website of the European Organization for Nuclear Research (CERN http://public.web.cern.ch/public/en/Science/ Recipe-en.html) and read through the pages indexed on the left. What was the role of the Higgs boson after the Big Bang? Go to CERN's press release page (http://press.web cern.ch/press) to see what's new in the search for the Higgs boson. (Note: The World Wide Web was invented at CERN.)

AG

Ankit Gupta

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Problem 59

Scientists debate whether there ever can be scientific evidence for a multiverse. A good example is a discussion in the journal Scientific American. Read the article "Does the Multiverse Really Exist?" in the August 2011 issue (it is probably accessible online through your school library) and the response at http://scientificamerican.com/article cfm? are some of the arguments for and against multiverses?

Sakib Sarker

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Problem 60

Clips from a four-part episode of the public television series NOVA called "The Fabric of the cosmos" can be accessed on PBS's website (http://pbs.org/wgbh/nova/physics/fabric-ofcosmos.html and complete episodes can be viewed on the Top Documentary Films website (http://topdocumentaryfilms.com/the-fabric-of-the-cosmos). Watch the clips or at least one of the episodes. Are the arguments made in these programs compelling? Is the science explained in a way that makes sense to a general audience?

Chris Johnson

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