Answer to Question #132102 in Astronomy | Astrophysics for Harshdeep

Question

Imagine that you live in a universe in which parallel lines eventually meet. what could you deduce about your universe from this?

Select all the answers that match
1) Ω>1
2)k is less than 0
3)The universe is infinite.
4)The universe will end in a Big Crunch.
5)If you travel far enough in a straight line, you will return to where you started.
6)The internal angles of a large enough triangle will add up to less than 180 degrees.
π is less than 3.14159265359... on large scales.

Answer 1

1) Ω>1 - true, because there is positive curvature

2)k is less than 0 - false, k=+1

3)The universe is infinite - false, the universe in this case is not infinite

4)The universe will end in a Big Crunch. - true

5)If you travel far enough in a straight line, you will return to where you started. - true, because the universe is closed

6)The internal angles of a large enough triangle will add up to less than 180 degrees. - false, it is more than 180 degrees.

7) π is less than 3.14159265359... on large scales - true; pi is not a constant any more, the ratio of circumference to its diameter depends on distance, but any ratio of circumference to its diameter will be less than pi in curved geometry.

Answer: 1), 4), 5), 7).