An Open Universe

Last time, we discussed what a flat universe was and what would happen to it. Today, we will focus on an open universe.


First, why is called an open universe? It's open because it does not come back in itself. This universe would be defined as being a negatively-curved space. What this means is that the universe curves away from itself. It may be difficult to imagine a 3-D negatively curved space, but you may know of a great example of a negatively-curved 2-D space: a saddle.

In the above image, the top portion of the saddle is curving up and away from the bottom portion, at 90° orientation. In the same way, the bottom section is curving down and away. and each flap are curving away from the opposite flap. In other words, all sections are getting farther and farther from each other and will not come together at any point in the future.

Also, if you were to draw a large enough triangle on the 2-D surface, the sum of the interior angles would always be less than 180° (recall for a flat space, the sum of the interior angles of a triangle equals 180°). Why is this? A straight line in negatively-curved space is not straight if you were to flatten out the space. As it appears in the above drawing, the lines look slightly concave, which leads to the next point.

Lines that start out parallel will gradually diverge. If you were to have two spaceships start out in space, moving parallel to each other, eventually, they will become farther and farther apart (in any direction).

So what does it mean if our universe is open? To have an open universe, the actually mass and energy density of the universe will have to be less than the critical density (the ratio between actual and critical is less than one). In other words, there is not enough mass and energy to allow gravity to overcome the expansion force of the universe. What will happen to our universe is that the expansion rate will accelerate and will never stop or slow down. The universe will continue to expand forever and will reach an age that eventually all matter will decay including the most stable of particles, protons. The universe will reach a state where the universe is just a soup of cold leptons and quarks and low energy radio waves. It will die with a whimper.

Next time, we will look at a closed universe.