Yes, this week astrophysicists made the slightly provocative claim that our entire Universe is a giant doughnut. And no, this isn't a pandemic induced mass delusion.

Let us begin with a little background information. For the past century scientists have been aware that space itself is curved in the presence of mass and energy, which is one of the basic principles of general relativity. In fact it is the curvature of space and time that creates the phenomenon that we perceive as gravitational forces. 

But then in the 2000s there were a series of experiments that measured the cosmic microwave radiation that was generated by the Big Bang (the most accurate of these being the Wilkinson Microwave Anisotropy Probe), and they found that on cosmic scales the Universe is flat. In fact it turned out to be so flat on the largest scales that new theories are needed to explain why it isn't curved at all - but that is a topic for another day.  The point is that the Universe is flat.

And this is where we reach a point of confusion for many physics and mathematics students, not to mention for the lay public. There are two different types of curvature, extrinsic and intrinsic. Extrinsic curvature means that an observed living outside of the surface can see the curvature. Intrinsic curvature means that an observed living inside the surface can perform measurements to study its curvature. For example, a cylinder has extrinsic curvature, but to a creature living inside its surface there is no difference between the cylinder and the plane. (You can test this by taking a flat sheet of paper and curling it into a tube. Although you are curving the surface, there is no point in the sheet of paper that gets stretched or compressed, and so it remains flat in any small given region). When we talk about space being curved, we mean intrinsic curvature. 

Which brings us to today's result. Astrophysicists from the Ulm University in Germany and the University of Lyon in France, did a new analysis of the cosmic microwave background (CMB), and proposed an interesting new result. The CMB contains various small regions in which the average temperature of the microwave radiation is slightly higher or slightly lower than the overall average. This can be caused by clumps of matter or by various other astrophysics phenomena, and those variations have been used for over twenty years to measure every aspect of the early Universe. In fact the CMB is arguably our best tool for studying the Big Bang and the evolution of the early Universe. 

According to the models proposed by this team, these perturbations in the CMB are not as large as they should be. If the Universe is infinite in scale, then the perturbations could get significantly larger. However if the Universe is actually shaped like a very large doughnut (or torus for the mathematically minded reader), then these perturbations will be limited in scale. One way to think about this is to imagine a wave travelling through space, with the perturbations representing the peaks and troughs in this wave. In an infinite Universe we can have waves of any size, but in a cylinder the waves will loop around and cancel themselves out unless the wavelength is significantly smaller than the size of the cylinder. And so if we live in an infinite Universe, we should see some very large perturbations, but if we live on a torus then there will be a limit to the size that they can reach.

And according to existing measurements of the CMB, there are no large perturbations. Adjusting for the expansion of the Universe since these variations were formed, it would seem that the Universe is only five to ten times larger than the observable Universe. (As an aside, because light travels at a finite speed there are regions of the Universe that are so far away that we cannot observe them. The age of the Universe is less than the time it would take light from those regions to reach us).

So do we live in a giant doughnut or not? The answer is that we really don't know. The lack of large perturbations in the cosmic microwave background make it possible, but it is equally possible that our detectors and analysis just missed the larger perturbations. Or it could be that some other yet unknown phenomenon in the early Universe put a restriction on the scale of the variations. There are even models in which our Universe is infinite, but a parallel Universe interferes with our own to remove the larger perturbations. 

So perhaps we do live on a giant doughnut. If only we could find an equally large cup of coffee to dip it in :)