Curvature of the Universe

Last time, we talked about how the universe might end since we really don't know what exactly will happen. There is not enough information for us yet to tell us whether the universe will come collapsing back in on itself or if it will just continue on expanding forever.


What do we know? We do know that the universe is nearly flat. By comparing the overall mass/energy density of the universe to what is called the critical density, we see that the ratio between the two (actual/critical) is very nearly one. As mentioned last time, a ratio less than one will result in an open universe, a ratio of one gives a flat universe, and a ratio greater than one will end up with a closed universe.


Both open and flat universes result in expansion continuing on forever, though a flat universe will asymptotically approach a physical limit for the size of the universe. A close universe will reach a maximum, then as gravity takes over, will begin to pull all matter and energy back towards each other.


Looking at the picture below, we see how the three types of universe relate to each other. The circled area is about where we are now, and you can see how it is difficult to tell if we are in an open universe, a flat universe, or a closed universe.

We can also describe the three different universes in reference to their shapes, which will go into more detail for the three. A flat universe is considered to have zero curvature, hence, it is flat like a piece of paper. Open universes have a negative curvature, like a saddle. Closed universes are said to positive curvature, like the surface of a sphere. Negatively curved space and positively curved space can lead to some strange phenomena which we will learn more about later.