21st Century Astronomy

Laura Kay, Stacy Palen, George Blumenthal

Chapter 22

Cosmology - all with Video Answers

Educators

Chapter Questions

Problem 1

If astronomers ignored any cosmological constant (or dark energy, 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.

Sarah Mccrumb

Sarah Mccrumb

Numerade Educator

Problem 2

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

Sarah Mccrumb

Numerade Educator

Problem 3

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 than the modern universe.

Sarah Mccrumb

Numerade Educator

Problem 4

According to the definitions of these terms in Chapter 1 superstring theory is
a. a hypothesis.
b. a theory.
c. a law.
d. a principle.

Sarah Mccrumb

Numerade Educator

Problem 5

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

Sarah Mccrumb

Numerade Educator

Problem 6

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.

Sarah Mccrumb

Numerade Educator

Problem 7

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.

Sarah Mccrumb

Numerade Educator

Problem 8

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

Sarah Mccrumb

Numerade Educator

Problem 9

Suppose you measure the angles of a triangle and find that they add to 185 degrees. 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.

Sarah Mccrumb

Numerade Educator

Problem 10

Put the following types of objects in order, starting with the first one to form after the Big Bang and ending with the last one to form.
a. neutral atoms, protons, nuclei
b. protons, nuclei, neutral atoms
c. nuclei, neutral atoms, protons
d. protons, neutral atoms, nuclei

Sarah Mccrumb

Numerade Educator

Problem 11

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

Sarah Mccrumb

Numerade Educator

Problem 12

Current understanding indicates that the universe (choose all that apply)
a. is closed.
b. is flat.
c. is open.
d. is inflating.
e. has accelerating expansion.

Sarah Mccrumb

Numerade Educator

Problem 13

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

Sarah Mccrumb

Numerade Educator

Problem 14

Observations of Type I supernovae in distant galaxies have shown that
a. the star formation rate in galaxies decreases with increasing redshift.
b. the expansion rate of the universe is increasing.
c. the cosmological constant is zero.
d. dark energy is negligible at the present time.

Sarah Mccrumb

Numerade Educator

Problem 15

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.

Sarah Mccrumb

Numerade Educator

Problem 16

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

Sarah Mccrumb

Numerade Educator

Problem 17

Describe the observational evidence suggesting that Einstein's cosmological constant (a repulsive force) may be needed to explain the historical expansion of the universe. Explain how Einstein was "right for the wrong reason."

Sheh Lit Chang

University of Washington

Problem 18

What do astronomers mean by dark energy?

Sarah Mccrumb

Numerade Educator

Problem 19

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?

Sarah Mccrumb

Numerade Educator

Problem 20

In Chapter 21 , we said we could estimate the age of the universe with Hubble time $\left(1 / H_{0}\right) .$ Why does that method not give the best answer?

Sarah Mccrumb

Numerade Educator

Problem 21

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

Sarah Mccrumb

Numerade Educator

Problem 22

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?

Sarah Mccrumb

Numerade Educator

Problem 23

Why is particle physics important for understanding the early universe?

Sarah Mccrumb

Numerade Educator

Problem 24

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?

Sarah Mccrumb

Numerade Educator

Problem 25

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?

Sarah Mccrumb

Numerade Educator

Problem 26

Explain the process of pair production.

Sarah Mccrumb

Numerade Educator

Problem 27

Describe the Planck era.

Sarah Mccrumb

Numerade Educator

Problem 28

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

Sarah Mccrumb

Numerade Educator

Problem 29

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

Sarah Mccrumb

Numerade Educator

Problem 30

Suggest another example of how a different value of a physical constant would affect conditions in a "parallel" universe.

Sarah Mccrumb

Numerade Educator

Problem 31

Study Figure 22.2
a. Is the vertical axis linear or logarithmic?
b. There are two labels for the horizontal axes. 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?

Sarah Mccrumb

Numerade Educator

Problem 32

Figure 22.3 shows a blue curve that indicates a model in which the universe first decelerated and then accelerated, as well as a red curve indicating continual 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?

Sarah Mccrumb

Numerade Educator

Problem 33

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 13.8 billion years)?

Sarah Mccrumb

Numerade Educator

Problem 34

Study Figure $22.8 .$ Is the plot linear or logarithmic? How much did the universe increase in size during the time of inflation? How much smaller was the universe at the beginning in an inflationary model than in the noninflationary model?

Sarah Mccrumb

Numerade Educator

Problem 35

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

Sarah Mccrumb

Numerade Educator

Problem 36

Study Figure 22.13
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?

Sarah Mccrumb

Numerade Educator

Problem 37

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

Sarah Mccrumb

Numerade Educator

Problem 38

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

Sarah Mccrumb

Numerade Educator

Problem 39

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 $\rho=\rho_{\alpha} / R_{\mathrm{U}}^{3},$ what was the scale factor of the universe when its average density was about the same as Earth's atmosphere at sea level $\left(\rho=1.2 \mathrm{kg} / \mathrm{m}^{7}\right) ?$

Sarah Mccrumb

Numerade Educator

Problem 40

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

Sarah Mccrumb

Numerade Educator

Problem 41

There are about 500 million CMB photons in the universe for every hydrogen atom. Using $E=m c^{2}$, what is the equivalent mass of these photons? Is it large enough to factor into the overall density of the universe?

Sarah Mccrumb

Numerade Educator

Problem 42

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 $\left(4.2 \times 10^{15} \mathrm{J}\right)$

Sarah Mccrumb

Numerade Educator

Problem 43

One GUT theory predicts that a proton will decay in about $10^{31}$ years, which means if you have $10^{31}$ 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 continual operation. What limit does this observation place on proton decay and on the GUT theory described here?

Sarah Mccrumb

Numerade Educator

Problem 44

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? Explain.

Sarah Mccrumb

Numerade Educator

Problem 45

To get a feeling for the emptiness of the universe, compare its density (about $9.9 \times 10^{-27} \mathrm{kg} / \mathrm{m}^{3}$ ) with that of Earth's atmosphere at sea level $\left(1.2 \mathrm{kg} / \mathrm{m}^{3}\right)$. How much denser is our atmosphere? Write this ratio using standard notation.

Sarah Mccrumb

Numerade Educator

Problem 46

Go to the website for the JINA Center for the Evolution of the Elements and watch the animation of Big Bang nucleosynthesis (http://www.jinaweb.org/movies/bangmovie.html). What are the major stages after the Big Bang? What elements are created? Why are heavier elements not created?

Ronald Prasad

Numerade Educator

Problem 47

Go to the website for the Dark Energy Survey, an international project that began in 2013 (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

Numerade Educator

Problem 48

a. Go to the website of the European Organization for Nuclear Research (CERN-http://home.web.cern.ch/ about/physics/early-universe) and read through the pages indexed on the right. What was the role of the Higgs boson after the Big Bang? (Note: The World Wide Web was invented at CERN.)
b. Citizen science: Go to Higgs Hunters (http://www higgshunters.org/) and log in with your Zooniverse account. Click on "Science" and watch the brief videos; keep going until "How you can help." Why do they expect that human eyes are more likely than computers to find exotic decays? Click on "Classify" and "Restart the Tutorial" to see examples of how to mark the images with "Off-center vertex" or "Something weird." Mark up a few images, keeping a record for your homework.

AG

Ankit Gupta

Numerade Educator

Problem 49

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/multiverse-the-case -for-parallel-universe. What are some of the arguments for and against multiverses?

Sakib Sarker

Numerade Educator

Problem 50

Clips and full episodes from a four-part series of the television show $N O V A$ called "The Fabric of the cosmos" can be accessed on PBS's website (http://pbs.org/wgbh/nova/physics/ fabric-of-cosmos.html). Watch 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?

Michael Anderson

Michael Anderson

Numerade Educator