Edited from an article by Paul Davies
To begin with the only hard fact we have on this topic: Nobody knows the structure or form of the universe. It’s debatable whether or not we will ever be able to know with any certainty. Still, the scientific process marches on. We observe the available evidence, and make intelligent guesses.
One fundamental question is whether or not the universe is infinite. Is there an edge, or does space and time just keep on going forever? We may never know, as we can only observe as far as the cosmic horizon. That is the point at which we can no longer see anything because there has not been enough time (in the 13.7 billion years of existence) for light to travel to, and be seen by earth. So it’s a bit like trying to determine the shape of the earth without being able to get out of your chair.
We have decided that there is no noticeable center to our universe. When we think of the Big Bang origin we picture an explosion happening in one spot, and everything spreading outwards from that spot. But that’s not really the case, according to the available evidence. The way that every galaxy is moving away from every other galaxy suggests the big bang happened everywhere-all-at-once.
The way we think about the space around us is in three dimensions. There are a very limited number of ways we can move, and we’re stuck being in only one place at any given time. In order to make sense of certain things, scientists are seriously considering that there are more dimensions than meets the eye.
One proposed shape for the universe, and a solution to the everywhere-all-at-once conundrum, is called a hypersphere. It’s a round ball, but rather than having a flat surface (like the earth) the outside edge of this ball is in itself a three dimensional space. Perhaps you could picture a balloon. There’s nothing on the inside, but the balloon wall is “thick” with three dimensions.
So now consider the Big Bang in context of this balloon being inflated. It starts as a little ball of solid latex. (that balloon, not the universe) As it is blown up, it expands outward and the hyperspherical wall grows. If you were to have dots on the surface of this balloon, all the dots would be moving farther away from all the other dots, just like our galaxies.
Note: While the balloon analogy hopefully helps to explain the affect of a hyperspherical universe and uniform expansion, it doesn’t get you any closer to actually picturing the true shape of a hypershpere.
So, that’s just one concept for the shape of the universe. With the hypersphere, there is a finite volume of space. In fact, if you could travel in one direction long enough, you would eventually loop around back to where you started. (like walking around the globe, but in a crazy 4-dimensional way)
Source – Paul Davies – Get a copy of his book The Goldilocks Enjgma