The general tendency of more distance objects to be "redshifted" strongly suggests that then universe is expanding.
Precisely in what manner this expansion is occurring with relation to the shape of space itself is unknown. These two fundamental issues about the nature of the universe are intrinsically linked.
The three main scenarios for the shape of the universe – and its expansion – are as follows:
1/ Spherical space
The curvature of space is spherical, and the universe will eventually collapse back on itself.
If two lasers are shone parallel to one another, their beams would eventually converge.
2/ Flat space
The curvature of space is flat – the universe has exactly enough mass to just prevent collapsing back on itself, and thus the universe will continue to expand – but only just.
If two lasers are shone parallel to one another, their beams would never meet.
3/ Hyperbolic space
The curvature of space is "saddle-shaped" – the universe will continually expand and never collapse back on itself.
If two lasers are shone parallel to one another, their beams would diverge from one another.
Now, the reason for this simple lesson in Cosmology is simple – I am a fan of the theory of hyperbolic space.
Now, "saddle-shaped" is difficult to envisage, so if you'd like to see what a hyperbolic universe might look like then do check out the The Virtual Minimal Surface Museum.
Check out the gallery – look at the images – and everytime you do, consider that you could very well be looking at a universe in miniature.
I'll include a couple of particular examples to get your imaginations moving:
