Is the Universe Open, Closed or Flat? The Horizon Problem, the Flatness Problem and Inflation

Abstract

We would very much like to know if our universe will keep expanding forever, as in the case of an open or flat universe, or whether the expansion will after some time halt and thereafter will reverse sign and become contraction, leading to a final “big crunch”. Crucially for answering this question is knowledge of how large the present mean density of matter and energy in the universe is (energy has an equivalent mass, given by Einstein’s formula E = mc²). As depicted in Fig. 8.4, open as well as flat and closed universes all start expanding from a very small and compact beginning. If for a closed universe the time when it reaches its maximum size is still very far in the future, it will at present be very difficult to distinguish the expanding Friedmann solution for this state from a flat or open one. The curves that depict the increase with time of the distances between galaxies for these three solutions are then at the present time very close to each other. To determine the precise shape of the curve that represents the increase of the distance between galaxies with time requires very accurate measurements of galaxy distances and redshifts, particularly for very distant galaxies, where the shapes of the curves for the three different Friedmann solutions begin to deviate from each other.

The “silly” question is the first intimation of some totally new development

Alfred North Whitehead (1861–1947), British-American philosopher