TOPOLOGY, COSMOLOGY AND THE SHAPE OF SPACE
3. Flat Universes
If the universe has Euclidean geometry (the usual geometry in which the
sum of the angles of a triangle is 180 degrees) then the universe is said
to be flat.
A 2-dimensional example of this is the flat plane.
Some think that the universe has this shape, only raised up a dimension.
In this model, the universe has Euclidean geometry, zero curvature, and
will expand forever (but just barely). In fact, a very popular model of
the big bang (the
inflation model) implies that the universe is
flat. This is an example of an open universe.
In this particular model,
the universe is infinite, but there exist flat models of the universe which
are finite, as we will see.
Goto Section 4.