Cosmic Perspective Fundamentals
3rd Edition
ISBN: 9780134988504
Author: Bennett, Jeffrey O., Donahue, M. (megan), SCHNEIDER, Nicholas, Voit, Mark
Publisher: Pearson,
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Textbook Question
Chapter 4, Problem 17SEQ
Explain all answers clearly, with complete sentences and proper essay structure, if needed. An asterisk (*) designates a quantitative problem, for which you should show all your work.
Explaining the Past. Test the nebular theory against each of the three hallmarks of science discussed in Chapter 3. Be as detailed as possible in explaining whether the theory does or does not satisfy these hallmarks. Use your findings to discuss whether it really is possible for science to inform us about how our solar system formed. Defend your opinion.
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Question 04
in 20
Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 4 Solutions
Cosmic Perspective Fundamentals
Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....
Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...
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