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RogerWaters

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- TL;DR Summary
- Untangling the effects of mass on the expansion and the curvature of the universe

Physics novice here reading pop sci cosmology. Please bear with me.

To my mind this means that the expansion and the shape of the universe are intrinsically linked? On first thought, this seemed strange to me as surely the universe could be expanding regardless of whether it is positive curved, negatively curved, or flat.

1. How are expansion and curvature related? This article states:

"If the actual density of the universe is less than the critical density, then there is not enough matter to stop the expansion of the universe, and it will expand forever. The resulting shape is curved like the surface of a saddle. This is known as an open universe."

2. But why should a universe that expands forever be negatively curved like a saddle? Why can't a flat universe continually expand?

Thanks.

*Premise 1*: Whether or not expansion is slowing down or speeding up depends on a battle between two phenomena: the attractive gravitational pull of matter and the repulsive gravitational push of dark energy. What counts in this contest is the density of each. (Also, the density of matter decreases as the universe expands because the volume of space increases). Basically: More mass, less/slower expansion.*Premise 2*: The spatial curvature of the universe is related to general relativity, which describes how spacetime is curved and bent by mass and energy. If all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed. The distribution of mass in the universe determines the curvature of space in Einstein's theory. Basically: More mass (per unit of space), more curvature.To my mind this means that the expansion and the shape of the universe are intrinsically linked? On first thought, this seemed strange to me as surely the universe could be expanding regardless of whether it is positive curved, negatively curved, or flat.

**Question time:**1. How are expansion and curvature related? This article states:

"If the actual density of the universe is less than the critical density, then there is not enough matter to stop the expansion of the universe, and it will expand forever. The resulting shape is curved like the surface of a saddle. This is known as an open universe."

2. But why should a universe that expands forever be negatively curved like a saddle? Why can't a flat universe continually expand?

Thanks.

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