1 How flat is the universe?
The curvature of space and our horizon radius are determined by the average density of the universe and its expansion rate. Cosmologists often say that space is nearly flat because the observed value of the density is close to the critical value for a flat universe. However, if the density was 2% more than the critical density, the horizon radius (yellow line) would be about 46 billion light-years and the radius of curvature of the corresponding hypersphere would be only 2.6 times greater. We would therefore see a modest but non-trivial portion of the hypersphere. If the density is exactly equal to the critical value, space is Euclidean, the radius of curvature is infinite and we can only see an infinitesimal portion of the universe.