Can we ever know the shape of the universe?

Launch in any direction and fly through the universe. Out of our solar system, beyond the edge of the Milky Way, through the forest of galaxies that make up our local group into the wilds of the distant cosmos, past black holes and galaxies and nearly infinite worlds… or are they infinite?

Could you keep traveling forever, or would you eventually reach an edge? Or maybe end up right back where you started? This is the biggest problem in cosmology, especially if you take the word “biggest” literally: what is the size and shape of our universe? We have a few hints, but they don’t point in any particular direction, so it remains largely a mystery.

When I talk about the universe with friends or colleagues, I often find myself reminding them that space is vast, perhaps even infinite. It’s hard to wrap your head around, but cosmologists and great thinkers have wondered about it for centuries. The best way to find out the size is to start by sorting out what shape it is. And there are many ideas for what shape our universe might take.

The simplest form of the universe would really be a flat sheet. It’s far more complicated than that, of course, but it’s a useful metaphor (as you can say about most things in physics). I’ll handwave past some of the technical details, but suffice it to say that if the universe is flat, all the geometry you learned in school works: Draw a triangle and the angles will add up to 180 degrees and all the lines will be straight. But if the cosmos is curved, things start to get funky. Your triangle wouldn’t be a triangle as you know it, but the effects would be so small you wouldn’t notice. The universe can be shaped like a hall or even like a sphere, and either way the geometry becomes non-Euclidean and therefore a bit strange.

The size and shape of the universe is controlled by two quantities: gravity and dark energy. The gravity of everything in the universe pulls it in, and dark energy pushes it to expand. If these two are perfectly matched, the universe is flat. If dark energy wins, it’s Pringle-shaped. Each of these forms would allow the universe to be finite or infinite – there are models that work for each.

If gravity wins, the universe is spherical and therefore finite – which is the simplest solution. But as far as we can tell from various large-scale observations of the cosmos, it appears that the universe is probably flat. Then again, recent observations have shown that dark energy can weaken over time, which really underscores how little we actually know for sure about the universe writ large. Dark matter is similarly mysterious, even as we build increasingly precise maps of it throughout the cosmos, and it is a crucial component of the universe’s gravity. So “probably flat” should still be taken with a grain of salt.

At this point I should tell you that I am not a completely unbiased narrator here. I, along with many physicists, do not like infinities. Sure, they’re fun to think about, but connect one to the physical world, and what does that really mean? Maybe it’s just the limits of my human brain, but I have a hard time accepting that anything can be meaningfully infinite. Everything must have some limit, even if that limit is extremely large. Infinity strikes me as a bit of a cop-out. There is no way to measure it. If our equations don’t work out right, will we just assume it goes on forever? Give me a break.

I’m not alone in that view, and given the general aversion to infinities, there are many theories about what a finite universe might look like. Although flat, there are many options for how different parts of space-time can be connected to each other – as I said, the sheet/sphere/saddle distinction is a simplification. First, there is the question of whether a finite universe must have an edge. If the universe is finite and flat like a sheet of paper, it must have one – but then we have to ask, what is beyond the edge? Maybe other universes, maybe nothing at all. It could be anything. But what happens right on the edge? Does existence just stop? It’s a little unnerving and hard to imagine, and it’s also hard to work your way into the equations that describe our universe.

If space-time is curved, the options open up a bit. A sphere doesn’t have an edge, so if you traveled too far in one direction, you’d just end up back where you started. Or it could be shaped like a donut or a Klein bottle or a strange sponge with a wormhole, or any number of other possibilities—some physicists have suggested it could be shaped like a peanut, a cone, or an apple, the last possible only by adding more dimensions than we currently exist in. Like I said, it’s complicated.

All the forms I just mentioned are finite. Add infinities into the mix and it all gets even wilder – one might even say unmanageable. You can travel forever and all you find is infinite space, an infinite variety of galaxies and star systems and worlds. There would be no concern about edges or what is “outside” the universe because everything would be inside it.

Somehow, the prospect is exciting. You can find anything out there. There will definitely be other life forms – just by pure probability – although that still mostly applies to a universe that is not infinite, but just very, very large. Personally, though, I can’t help but think that an infinite amount of universes is just too much. I love to imagine what could be out there, but if the answer is “anything is possible because the universe goes on forever and ever”, there seems to be no point in imagining.

Those are personal feelings though, and like everything in physics, it will ultimately come down to observations and math. That’s part of what I love about physics, its concreteness – and infinity just isn’t concrete enough. If I choose a direction and fly off through the universe, I will eventually reach something, whether it’s an edge or just back home.

Mysteries of the Universe: Cheshire, England

Spend a weekend with some of the brightest minds in science as you explore the mysteries of the universe in an exciting program that includes an excursion to see the iconic Lovell Telescope.