Is the universe doughnut shaped?

Cosmic topology is actually a term used to describe attempts to determine the overall structure of the Universe, and it’s stumped scientists for years. Is the Universe a flat sheet, which researchers dub, “boring”, or are bits of it connected back into themselves, like a doughnut? A new international partnership called Compact is attempting to get to the bottom of it, and Andrew Jaffe, at Imperial College, is part of the team. I've been speaking with him to hear more about the problem they’re grappling with, beginning with getting my head around the difference between “shape” and “topology”…

Andrew - Shape can mean lots of different things in lots of different contexts. And even in cosmology and astrophysics, it can have more than one meaning. So we have to be very precise and that's why we use this word topology. So let's step back and think about the different shapes that things can have. Well, they can be round and curved. They could be flat and have sharp edges. And the part that's about curvature, we think of with a different word, geometry. So the geometry talks about how curved a surface is, for example. So a ball has a particular kind of surface. A saddle has a surface, a sheet of paper has a curvature. All of these things have curvature and therefore geometry. What we're asking here is not about the curvature of the universe, which is a different question, but the topology of the universe and the topology is about, well, it's sort of about holes and handles and the way different places in the universe are connected to each other. So the best way to think about this is to think about a video game. So remember the kind of video game where the character goes out the right hand side of the screen and comes right back in the left hand side of the screen or goes out the top and comes right in the bottom? Well, the screen is flat, it has a flat geometry, but it's connected by the left and the right and the top and the bottom. And that's the topology. And what's weird about that is that it's the topology of the surface of a doughnut or a bagel. Now think about that. So take the two edges of the screen, the right and the left edge, and curl them around so that they meet. And now you have a tube. Then take the top and the bottom and curl those around those circles that you've made by curling the left and right together. Take those and make a bagel. And that's the kind of thing that we're searching for, but not on a two dimensional screen, but in three dimensions where now not only do you have left and right and top and bottom, but you have front and back. But you can do the same geometrical and topological manipulations and make something which is like an extra dimensional doughnut or bagel. And we call that surface in general a Taurus.

Chris - And why do we think that the universe might have one of these exciting topologies? It's not just a flat, smooth thing blowing up like a balloon.

Andrew - The simplest answer is why not? There's nothing in the physics that we know to tell us what the topology of the universe should be. So Einstein's theory of general relativity, which is about gravity and also dictates the expansion of the universe that you just mentioned, says nothing, literally nothing, about the topology of the universe. So we need to check because there's no reason not to have it. And if you look at the way quantum mechanics and general relativity, that is to say the science of the very small and the science of gravity and the very large interact, then we have at least some reasons to believe that in the very, very, very, very, very early universe, 10 to the minus 43 seconds or so old, that that's when topology might have been very fungible, very changeable. It could just change because of quantum mechanics. And that the most likely thing would be a small universe that is small in exactly the same way that this Taurus is small. That the left and right and top and bottom and front and back are continuous with each other. And you get these Taurus like shapes.

Chris - And how is Compact trying to get underneath this?

Andrew - Well, we cosmologists more generally have been looking for the kinds of effects that an interesting topology might give us in our data for at least 75 years. And the first way we looked at it was, if you go back to this video game, if you're living in the video game and you look to your left, you'll see the back of your head. Where you look up, you see your feet. There's no reason why your line of sight doesn't just keep going. And so that's the same thing we look at here. So originally people just looked for duplicates of the local universe far away. So they say, do we see the Milky Way millions or billions of light years away? And of course that's a hard observation to do, but nonetheless people have said, no, we don't think we see that happening. So then somewhat more recently, since about 1990, we have actually gotten hold of the most distant pictures of the universe we can possibly get by looking at something called the cosmic microwave background radiation, which is light from about 400,000 years after the Big Bang, so almost 14 billion years ago. And what we want to do then is look for repeated patterns on that surface of the sky. And we also don't see them there. But it turns out that this Taurus that I mentioned, this doughnut shape, the surface of this doughnut, is not the only topology you can make. There are, roughly speaking, 18 different topologies that even if you're just living in a geometrically flat, no curvature universe, you can have. And then if you allow the universe to have curvature, there are literally infinitely many more possibilities. So part of our job is that kind of fun maths job. But what we really want to do is go beyond that. We want to say, are there observations we can make that might give us further hints on the topology? And the answer to that is we think yes. So our nearby universe, if you can look at things on a fine enough granularity and you can do a census of essentially everything inside the CMB, then that gives you hints about the way things are distributed, even outside what you can see. That's sort of the place that we're just getting to now, to come to grips with how we might do those observations using some future observatories and their successors. Because even the near the near future observatories probably won't be enough, but they're successors, which will enable us to do a census of everything or almost everything that's in the visible universe.