Doughnut-Shaped Universe Back In the Race

SpaceAdmiral writes "The once-popular idea that the universe could be small and finite is making a comeback. Many researchers thought that a 'wraparound' universe would mean that distant objects would be seen multiple times in the sky, but new research suggests that a '3-torus' (or 'doughnut universe'), as well as other shapes, could fit our actual observations, particularly the WMAP data."

Comments

Re:That's silly.

[wass]

It's primarily the boundary conditions that are leading to the 3-torus idea.

A torus gives periodic boundary conditions in two dimensions. Periodic boundarty conditions for one axis can be thought of as curling a piece of paper around to make a cylinder. For someone on this paper, picture running on a soccer field, and if you run out of bounds on the left side you pop back in in the right side, aka pacman's tunnel. To make a torus, you'd need to wrap the top exposed circular edge to the bottom circular edge, in a donut way. You'd need to bend the paper to do this, so you'd really need something like a rubber membrane. But once you connect this, then you have a soccer field where when you kick a ball behind your opponent's goal, it comes out from behind your goal. That is 2-D boundary conditions. The simplest shape that can manifest these boundary conditions of a two-dimensional system is a torus, which exists in 3-D.

Now extend this one step further. Take a 3-D space, and add periodic boundary conditions for left/right, back/front, and also top/down. This is the 3-torus that is discussed in the article. Someone confined to this 3-D surface has a full three independent degrees of freedom for movement, but the manifestation of this shape would look more complicated in four or five dimensions. But that is what is being talked about here.

Of course in quantum cosmology there are other dimensions, such as the warped 5th dimension of the Randall-Sundrum model , which may or may not be periodic, and add to very peculiar topologies of the universe.