Can we ever know the shape of the universe?

Start in any direction and fly through space. From 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 a limit? Or maybe you’ll end up where you started? This is the biggest problem in cosmology, especially if you take the word “biggest” literally: what exactly 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 space with friends or colleagues, I often find myself reminding them that space is vast, perhaps even infinite. It’s hard to navigate, but cosmologists and great thinkers have puzzled over it for centuries. The best way to figure out its size is to start by sorting out what shape it is. And there are lots of ideas about what our universe could look like.

The simplest shape for space would essentially be a flat sheet. Of course, it’s much more complicated than that, but it’s a useful metaphor (which you could say about most things in physics). I’m hand-waving over 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 its angles will add up to 180 degrees and all its lines will be straight. But if the universe is curved, things start to get weird. Your triangle would not be a triangle as you know it, but the effects would be so small that you wouldn’t notice them. The universe could be shaped like a saddle or even a sphere, and either way, the geometry becomes non-Euclidean and therefore a bit odd.

The size and shape of the universe is governed 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 the two are perfectly aligned, the universe is flat. If dark energy wins, it’s shaped like a Pringle. 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. However, as far as we can tell from various large-scale observations of the universe, it appears that the universe is probably flat. Then again, recent observations have shown that dark energy can decay over time, really underscoring how little we really know for sure about the vast universe. Dark matter is similarly enigmatic, even as we create increasingly accurate maps of it throughout the universe, and 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 impartial narrator here. I, like many physicists, do not like infinities. Sure, they’re fun to think about, but plug them into the physical world and what does that even 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 a limit, even if that limit is extremely large. Infinity feels a bit like a cop-out to me. There is no way to measure it. If our equations aren’t working right, are we just going to assume it’s going to last forever? Give me a break.

I’m not alone in this opinion, and given the general distance for infinities, there are plenty of theories about what a finite universe might look like. Even though it’s flat, there are lots of possibilities for how different parts of spacetime can be connected to each other – as I said, the leaf/sphere/saddle distinction is a simplification. For one, there is the question of whether a finite universe must have an edge. If the universe is finite and flat as 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 can be anything. But what happens right at the edge? Existence just…stops? This is a little unnerving and hard to imagine, and also hard to work into the equations that describe our universe.

If spacetime is curved, the possibilities open up a bit. A sphere has no edge, so if you traveled too far in one direction, you would end up where you started. Or it could be shaped like a donut, or a Klein bottle, or a strange mushroom with wormholes, or any number of other possibilities—some physicists have suggested it could be shaped like a peanut, a pinecone, or an apple, the last of which is only possible by adding more dimensions than we currently exist in. Like I said, it’s complicated.

All those shapes I just mentioned are done. Add infinities to the mix and things get even wilder – one might even say clumsy. You could travel forever and all you would find is an infinite universe, an infinite variety of galaxies and star systems and worlds. There would be no concern about the edges or what is “outside” the universe because everything would be inside.

In a way, the prospect is exciting. You can find anything there. There would certainly be other forms of life – just by mere probability – although this is basically still true for a universe that is not infinite but really, really big. Personally, though, I can’t help feeling that the infinite amount of space is just too much. I like 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 no point in imagining.

However, these are personal feelings and like everything in physics, it ultimately comes down to observation 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 through space, eventually I want to reach something, whether it’s the edge or just home again.

Mysteries of the Universe: Cheshire, England

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

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