# What Is the Shape of the Universe?

(Last Updated On: February 3, 2020)

We all know the universe is big. Like, really big. And if you keep up with this Blog, you know the universe has a color, and you also have an idea of when the universe might end. But beyond that, how much do you really know about it? For example, have you ever stopped to think about the shape of our universe? Is it a big sphere? A flat plane? Something else entirely?

Sadly, we’re lacking the expensive astronomy equipment to come to our own conclusions here. So we’ll break down what the research tells us.

## Einstein and the Shape of the Universe

Thanks to general relativity, we know we exist in four dimensions. There are the three that you move through space in (left/right, up/down, back/forward). Then there is also time. Just as a caveat, we don’t really control our movement through time in the same way that we can control how we move through space. We only get to go forwards through time. Anyway, this is all modeled in the concept of spacetime

So spacetime, which is basically where we exist, is not exactly flat. Spacetime can be curved by mass. This curve becomes more prominent with objects of significant mass–think stuff like stars and black holes.

The long short is that thanks to some super complicated physics, we know that the universe is curved.

## Density of the Universe

So we know the shape of the universe is going to involve some curve. If we want to figure out what the universe is shaped like, we’re going to need access to some more dense physics. Some would say it’s quite critical knowledge.

Actually it’s just called critical density and it is dense physics. Density is an expression of mass over volume, so to calculate the density of the universe, you just take the mass of the universe and divide it by how big it is.

Except, the universe is ever expanding, something we’ve touched upon in our other universe posts. You don’t need to know much more than the fact that the universe has been expanding since it was born and it doesn’t seem to be stopping anytime soon.

As such, the critical density is the density of the universe that would just stop its expansion. Though that could end up having a little something to do with how the universe will end.

The universe’s critical value, by the way, is about 10^-26 kilograms per cubic meter. Which is about the same as having 10 hydrogen atoms per cubic meter. Suffice to say, not very dense.

## Shaping the Universe

Turns out we have to make assumptions about the universe if we want to know its shape. Assuming the universe is finite and has boundaries, there are three possibilities on the table right now, though we can rule one of them out. Our options are a sphere, a hyperbolic paraboloid, and a flat surface. We can rule out the flat surface because that implies a universe at critical density.

After that our concern goes to how dense the matter of the universe is. If it’s high, you have a closed universe of positive curvature. This gives us a hollow sphere, and we mostly exist on the inside of that sphere.

In the exact opposite scenario with less dense matter, you get a hyperbolic paraboloid, which looks like this kind of weird 3-D ‘U’.

### Boundless Universe?

There are shapes of finite volume with no edges, which gives us the shenanigans of the 3-sphere and the 3-torus. The two are really hard to visualize if you’re not into advanced physics or 3-d calculus, so just suffice to say it’s weird.

Given that we’re pretty sure the universe isn’t at its critical density, let’s just go on assuming we’re in a sphere or a hyperbolic paraboloid?

Shapes are hard so here are a bunch.