Explanation of expanding universe

[SBMDStudent]

I once asked a physicist to explain what the universe expands into, and he gave me the analogy of raisins in bread dough. That the raisins represents galaxies, galactic clusters, etc...and as the universe (bread dough) expands, the galaxies (raisins) move apart. But this analogy assumes that the bread dough expands into the air around it, so I'm still unclear on what the universe is said to expand into.
Can anyone clarify? Thanks in advance!

 

[Dale]

We have no evidence to support the idea that there is anything that the universe is expanding into.

 

[tom.stoer]

Mathematically it's quite simple: the universe is described by a 3-dim. expanding manifold without boundary (a 2-dim. manifold without can be visualized as an infinite sheet of paper, a surface of a balloon, a surface of a donut, ...); this mathematical concept does not require any embedding space, so the 3-dim. manifold can be described mathematically without a higher dimensional space into which it is embedded and into which it expands (a 2-dim. surface of a balloon can be described without the embedding into the 3-dim. space we ar used to).

So the only problem is that your everyday experience confused you b/c you are not able to think about these manifolds and their expansion w/o thinking about an embedding (whereas mathematically this embedding is not required).

So a 2-dim. model of our 3-dim. expanding universe would be a 2-dim. expanding sheet of paper with stars, galaxies, ... on this sheet of paper - but without the 3-dim. space into which the sheet is embedded.