Most astronomers think that the universe is infinite, but recent measurements suggest that it could be finite and relatively small. Indeed, as Jean-Pierre Luminet describes, we could be living in an exotic universe shaped rather like a football.
At a Glance: Cosmic topology
• There are three possibilities for the curvature of the universe: space can be flat, spherical or hyperbolic
• The geometry of the universe depends on its curvature and also on its topology, which governs the way space is connected and so determines if it is finite or infinite
• Measurements of the cosmic microwave background constrain the curvature of the universe and provide hints about its topology
• Recent data suggest that the universe might be multiply connected, like the left- and right-hand sides of the screen in a computer game
• Since the early 1990s the number of cosmo-topologists around the world has grown to more than 50
Read more... (Physicsweb)