
Concept explainers
(a)
The distance between two clusters at the point in time when light was emitted from HS 1946+7658 to produce an image on Earth tonight. Suppose that the distance between two clusters of galaxies is
(a)

Answer to Problem 42Q
Solution:
Explanation of Solution
Given data:
The redshift for the quasar HS 1946+7658 is 3.02.
The distance between two clusters in present day universe is
The density of matter in today’s universe is
Formula used:
The distance between the two clusters when light was emitted from a quasar is:
Here, z is the redshift.
Explanation:
Recall the expression for the distance between the two clusters:
Substitute 3.02 for z and
Conclusion:
Therefore, the distance between the two clusters is
(b)
The average density of the matter
(b)

Answer to Problem 42Q
Solution:
Explanation of Solution
Given data:
The density of today’s universe is
The redshift for the quasar HS 1946+7658 is 3.02.
Formula used:
The relationship between redshift and average density is:
Here,
Explanation:
Recall the relationship between redshift and average density.
Substitute 3.02 for z and
Conclusion:
Therefore, the average density is
(c)
The temperature of the cosmic background
(c)

Answer to Problem 42Q
Solution:
Explanation of Solution
Given data:
The redshift for the quasar HS 1946+7658 is 3.02.
Formula used:
The relationship between the mass density of radiation and the background temperature is:
Here,
Explanation:
The temperature of the background radiation would have been 4.02 times greater because the expansion of the universe increased by a factor 4.02
So, the background temperature is:
Recall the relationship between mass density of radiation and background temperature.
Substitute
Conclusion:
Therefore, the mass density of radiation is
(d)
Whether the universe was matter-dominated, radiation dominated, or dark energy-dominated in the distant past, at the point in time when light was emitted from HS 1946+7658 to produce an image on earth tonight. Suppose that the distance between two clusters of galaxies is
(d)

Answer to Problem 42Q
Solution:
Matter dominated
Explanation of Solution
Given data:
The redshift for the quasar HS 1946+7658 is 3.02.
The distance between two clusters in the present-day universe is
The density of today’s universe is
Formula used:
The relationship between redshift and average density is:
Here,
The relationship between mass density of radiation and background temperature is:
Here,
Explanation:
The average density
The mass density of radiation
From these results, it is concluded that
Conclusion:
Therefore, the universe was matter dominated.
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Chapter 25 Solutions
Universe
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