Understanding Our Universe
Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 16, Problem 18QAP
To determine

The significance of flatness problem.

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What will happen if the density of the universe is less than the critical density?
1. The current (critical) density of our universe is pe = 10-26kg/m³. Assume the universe is filled with cubes with equal size that each contain one person of m = 100kg. What would the length of the side of such a cube have to be in order to give the correct critical density? How many hydrogen atoms would you need in a box of 1 m³ to reach the critical density? The matter we know, which consists mostly of hydrogen, constitutes only 4.8% of the current critical energy density of our universe. So how many hydrogen atoms are actually in a box of 1 m3 in our universe? Deep space is very empty and a much better vacuum than we can obtain on earth in a laboratory.
The present number density of electrons in the Universe is the same as that of protons, about 0.2 m-3. Consider a time long before the formation of the microwave background, when the scale factor was x times smaller than its present value.  What was the number density of electrons then? Value: x = 12×106
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