If the density of the Universe is just right, the Universe is flat. If the density of the Universe is small, the Universe is negatively curved. If the density of the Universe is large, the Universe is positively curved. Locally, space curves in response to mass, so it makes sense to think that the density of mass in the Universe would determine the universal curvature. So, though it would work in principle, it will not work in practice.īut, think about what we are talking about. clusters and walls), as well as the fact that the Universe is not static, but changes over time, and looking back a certain distance is the same as looking back a certain time. ![]() This would work in principle, but there are so many complicating factors (such as non-uniform distribution of galaxies, i.e. If the number of galaxies changes between circles at different distances, you may be able to figure out if you are in positive or negative space, as opposed to flat. To do this, you look at all the galaxies within a circle at a certain distance. But we could do galaxy counts, which will tell us how the area of a circle changes with radius. Parallel lines diverge, the angles of a triangle add up to less than 180 degrees, and the circumference of a circle is less than 2 R.įor our Universe, the space is too big for us to use the geometrical tests, like measuring the angles of a triangle. A negatively curved space is infinite, has no boundary, and no center. Negative Curvature You can't even draw or imagine a 2-D negatively curved space, but on small scales, it looks like a 'Pringle'.Parallel lines stay parallel, the angles of a triangle add up to 180 degrees, and the circumference of a circle is equal to 2 R. The geometry in a flat space is the kind of geomtry that you are used to. A flat, 2-D space is infinite, unbounded and has no center. ![]()
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