The Flat Universe

A flat universe may be the easiest type of universe to imagine. We define a flat universe as a universe that has its mass/energy density equal to the critical density. The critical density is the density required to cancel out the expansion of the universe with gravity. In other words, a flat universe will expand at an ever slowing rate as the universe will reach a maximum size at some time in the infinite future. We call this asymptotic expansion. It will never quite reach the maximum size but approaches it without ever shrinking.


Flat universes are also defined as having zero curvature. Imagine a piece of paper that is infinitely large. The paper is flat in 2D, while the universe is flat in 3D, but they are similar. In a flat universe, if you start out at any location, there is no way to reach your original location without turning. If you start out in a straight line, you will remain on that straight line forever.


Another thing about flat universes is that if you draw two lines parallel to each other, the lines will always remain parallel. Two spacecraft travelling parallel to each other will always remain the same distance apart no matter how far they travel.


The sum of the angles in a triangle will always equal 180°, no matter how big you make the triangle. If you know anything about geometry, you know this is true. However, when we get into open and closed universes, you'll see how this "constant of geometry" will vary.

1. Flat universes have actual densities equal to the critical density, i.e. the ratio between the two is always equal to one.
2. Flat universes have zero curvature, hence the term flat.
3. The ultimate fate of a flat universe is it will asymptotically approach a maximum size based on the critical density, but will never reach the maximum size, yet will never shrink in size.
4. Parallel lines will always remain parallel, no matter how far the lines reach from their starting points.
5. Triangles always have the sum of its angles equal to 180°.

Next time, we'll discuss an open universe.