edpell said:
What is the definition of a universe being closed?
Usage of the terms "closed", "flat", and "open" changed around year 1998 when it was realized that the universe could be
spatially closed (in the sense of overall positive spatial curvature, like a hypersphere, or the idea finite spatial volume) and yet
even though it was spatially closed it could continue expanding forever.
Before 1998 when you looked into pop cosmo books you would see a very neat and misleading triple package.
A:"closed" meant spatially closed and also the (wrong) idea that she has to end in a crunch
B:"flat" meant spatially flat, zero spatial curvature, and also the connotation that she keeps expanding but at a diminishing rate that is just barely fast enough to avoid re-collapse.
C:"open" meant negative spatial curvature, typically an infinite spatial volume, and also carried a connotation about future expansion
The explainers always locked you into associating some future expansion (or contraction) scenario with each separate spatial configuration. But it doesn't have to be that way.
After 1998 everybody recognized it wasn't that pat and simple---that with a positive cosmological constant, or equivalently with dark energy, you could have an expansion scenario more or less independent of which spatial configuration.
So closed has come to mean (at least for some of us)
spatially closed. And it doesn't mean you have to end in a crunch.
The typical picture of a closed universe is the hypersphere, the 3d analog of a 2d surface of a sphere. The 2D toy model analogy can be pictured as the surface of an expanding balloon. But all existence is concentrated on the geometrical surface of the balloon. There is no rubber, there is no inside-the-balloon or outside-the-balloon. All that exists is 2d stars and 2d creatures on the 2d surface.
And then to get the real world you jack that picture up from 2 to 3d.
Matter is roughly uniformly distributed over the whole of space---back in the toy model case that means over the whole 2d surface of the balloon. There is no outside-the-universe. No edge. No boundary. A finite 3d volume, just like in the 2d toy model there is a finite 2d area (of the surface of the balloon).
You asked what does "
closed universe" mean. I think that is about it. Spatial closure, edgelessness, finite volume, finite circumference. I'd like to hear Dmitry's definition, though. In my experience he's reliably informed clear and concise.
If you have problems with anything I or anybody have said, keep asking questions.
