Homework help - universe density & curvature

AI Thread Summary
The discussion focuses on calculating the radius of curvature and maximum distance in a universe with a mass density of 10 protons/m3. The first part of the problem is understood, but the second part regarding maximum distance remains unclear. The Friedman equation indicates a maximum scale factor of 10/9, and the universe is identified as matter-dominated with positive curvature. It is suggested that instead of asking for maximum distance, one could determine the distance needed to return to the starting point, which would be half of the maximum distance. The final step involves calculating the radius of the 3-sphere at maximum expansion to find the answer.
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1. If the current mass density in the Universe was about 10 protons/m3 what would be the current radius of its curvature? What would be the maximum distance between the two points in the Universe?
I got the first part but not the 2nd. If I solve the Friedman equation I get the max scale factor to be density/(density -1) which in this case is 10/9. Again I'm posting here because last the people in the homework help section don;t know much cosmology. Do I need to solve for the Hubble distance for this universe. btw this is a matter dominated universe with positive curvature.
 
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Well, this is the geometry of a 3-sphere. So instead of asking the maximum distance, why not ask what distance would have to be traveled in order to come back to where you start? The maximum distance between any two objects will naturally be half that.

All that remains after that is figuring out the radius of this 3-sphere at maximum expansion, and you should have the answer.

Does that help?
 
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