Good question! The answer is nothing, there is no inside. But perhaps that requires some explanation.
When we say the universe has some shape, what we mean is that it
has some geometric features similar to an object that shape. Now the
universe would not be (spatially) like a 3-dimensional sphere, but
perhaps like the 3-dimensional surface of a 4-dimensional sphere.
That's hard to picture. What features would our universe have in common
with that sort of figure, which does have a hard-to-picture inside. If
it turns out to be true that our universe is 'spherical' that means
that every circle has a circumference that's smaller than 2*pi*radius,
just like the circles you draw on the 2-d surface of a 3-d sphere. By
"radius", we mean the distance you'd measure if you traveled from the
center of the circle out to the perimeter, all the while staying on the
2-d surface of the 3-d sphere. Furthermore, just like those circles,
our circles would each have the same circumference/radius ratio for a
particular length of radius. Bigger radii give smaller
A geometrical space can exhibit these properties purely on its own,
without having any other points forming an 'inside'. Unless somebody
figured out some more general description of the universe than anything
we now have, we wouldn't even know what it would mean to say that there
were points inside.
I realize that this must sound extremely obscure. The key idea is
that when we describe the geometry of the universe we are making claims
only about relations between points (or events) in it. The figures like
surfaces of spheres that are sometimes used in descriptions are
intended only to help us picture those relations among points in our
universe. The other points that happen to show up in our picture
analogy don't have any corresponding points in the real thing, so far
as we know.
(published on 10/22/2007)