Space and Physics
PUBLISHED

# The Earth Is Not Flat But The Universe Might Be

Among the many mysteries of the universe there is one that is deceptively simple and yet strikes at the very heart of our ignorance of the cosmos: what is the shape of the universe? To come to the correct answer, we need to solve the mysteries of dark matter and dark energy and some other pretty crucial problems — and we don’t have the tools to do that just yet.

So, for now, we have the best guess: The universe, as far as we can tell, is 3-dimensionally flat. Now, this doesn’t mean we live in Flatlandia or that somehow the Earth is flat (it really isn’t). It’s about the geometry of the universe, and the flat universe has a very simple geometry, something you might have encountered in math lessons in school: two parallel lines in this universe will never meet, and the sum of the interior angles of a triangle is always 180 degrees.

The geometry of the universe is estimated from the properties of the various components: electromagnetic radiation, regular matter, dark matter, and dark energy. If the sum of all the densities of these matches a precise number, called the "critical density", the universe is flat. A value lower or higher produces very different geometries, as you can see below.

If the density of the universe is less than the critical density then the shape of the universe is akin to a saddle or a pringle (if the universe was 2-dimensional). In that universe, two parallel lines not only never meet but grow further and further apart. This is known as an "open universe".

On the other side of the critical density, there is the "closed universe". The universe in this case has a geometry that has a 2D equivalent to the surface of a sphere. This doesn’t mean that the universe is a big ball, these are just ways for us to understand the complexity of 4-dimensional geometry using something we are familiar with.

In a closed universe, parallel lines meet twice. This might seem completely wrong, but it is easy to picture it. Just imagine the meridians, the lines that provide the longitude of a location on Earth. These lines are all parallel to each other at the equator. But they will converge at the North and South Pole.