Homework help - universe density & curvature

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SUMMARY

The discussion focuses on calculating the radius of curvature and maximum distance between two points in a matter-dominated universe with a density of 10 protons/m³. The Friedman equation is utilized to determine the maximum scale factor, yielding a value of 10/9. The geometry is identified as a 3-sphere, and it is concluded that the maximum distance between two objects is half the circumference of the sphere. The key takeaway is that understanding the radius of the 3-sphere at maximum expansion is essential for solving the problem.

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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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