Curved Spacetime

Our calculation for the expansion dynamics was Newtonian. Using General Relativity, a similar calculation gives an identical answer, but also gives meaning to k: the curvature of space. Space need not be Euclidian!

Remember our analogy for the expansion of ants on an expanding balloon. Keep thinking along those lines.

We have three options for curvature:

k=1: positive curvature (like a ball)
k=0: zero curvature (flat like paper)
k=-1: negative curvature (saddle-like)

(courtesy Syracuse University)

In non-Euclidian space, distances and sizes do non-intuitive things. This allows us to make observational tests of cosmology!

But remember, this is a three-dimensional analogy to what is really happening to space. Like all analogies it can only be pushed so far...