Is the Universe Infinite? The Surprising Truth About Cosmic Geometry

Observations show the universe appears flat, yet its true size and global shape beyond the observable horizon may remain forever unknown.

The surface of Earth has a measurable size. Scientists can calculate its total area, and if the planet were expanding, we would see its dimensions steadily increase over time.

Because Earth is something we can directly study, it also offers a helpful analogy for thinking about what might exist beyond the limits of the observable universe.

What lies beyond the cosmic horizon

Astronomers generally assume that the universe continues beyond the boundary we can observe. In other words, if our telescopes could see farther, we would likely find additional galaxies, stars, and cosmic structures stretching outward. The idea is similar to standing on Earth and looking toward the horizon. We cannot see the entire planet at once, yet we know more of it lies beyond the distance visible to our eyes.

This leads to a deeper question: how large is the universe as a whole, including the regions beyond what we can detect? In reality, scientists may never know the full answer. The observable universe represents a hard boundary for information. It limits not only what we can see, but also what knowledge can ever reach us. The universe contains a finite amount of information that could potentially arrive within our region of space, even if we waited indefinitely into the future.

All we can do is guess.

It’s totally possible that the universe is infinite. It just goes and goes and goes without end, forever.

But it’s also possible that it’s finite. But how can a finite universe still not have an edge? Well, how can the surface of the Earth be finite and yet not have an edge?

Curvature allows finite without edges

Yes, it has an edge in the third dimension – we call it outer space. But again, that’s cheating! The two-dimensional surface is both finite and borderless, and it accomplishes that seemingly paradoxical feat by being curved.

We know the surface of the Earth is curved. We can measure it without our feet ever leaving the ground. In mathematics, we can build a few tools to give us a clue as to the geometry of the Earth. One tool is triangles. On a perfectly flat plane, when you draw a triangle, the interior angles add up to 180 degrees. Thank you, Euclid. But if you were to bust out a giant marker, pick three random cities, and draw giant lines connecting them, you would end up with a triangle with interior angles greater than 180 degrees.

The other is through parallel lines. On a flat plane, parallel lines never intersect. But on curved surfaces, they do. If you and me start and the equator and follow straight lines moving north, we will eventually intersect at the north pole. Not because we turned, but because the Earth curved underneath us.

The cosmic microwave background test

We can play the same games in the universe. We look at the light from the very early universe, from a special event when the cosmos cooled from a hot, dense plasma and released a flood of radiation, known as the cosmic microwave background, or CMB.

The physics of that plasma is actually pretty straightforward (we have a decent understanding of plasmas here on Earth), and we know from our calculations that there should be slight variations in temperature from place to place across the CMB. And wouldn’t you know it, there are!

Plus, we can calculate how big those splotches ought to be. If the universe is curved, then the path of light should have bent as it traveled all those billions of light-years. We then compare how big they are to how big we expect them to be. If they are different sizes, then we know the universe is curved.

They’re exactly the size we expect them to be. And that’s how we know the universe is flat.

Flat does not mean infinite

Case closed? Is the universe infinite? Not so fast.

If we were to attempt to measure the curvature of the Earth from, I don’t know, your neighborhood, we wouldn’t have much success. If your triangles are too small or the parallel lines too short, then you won’t be able to get a sense of the overall curvature. We are limited in our measurements to our observable bubble. And within that bubble everything seems as flat as flat can be.

So maybe the universe is curved, but on much, much larger scales than our tiny little observable patch (I know that tens of billions of light-years isn’t exactly tiny, but it is compared to how big the universe COULD be).

It’s entirely possible that the universe curves back on itself. That would mean you could travel in one direction long enough and eventually reach your starting point, just like on the Earth. But you would have to travel beyond the horizon, which in an expanding universe is impossible, so this is only possible as a theoretical exercise.

Flat geometry, strange topologies

And you know what’s really wild? I promise this is the last piece of forbidden chocolate. The universe could be flat and STILL be curved. Check it out. Take a flat piece of paper and draw some triangles and parallel lines on it. Now bend it into a cylinder. Those triangles are still triangles, and those parallel lines are still parallel.

This is the difference between geometry and topology. The geometry of the universe appears to be flat. But one or more dimensions could be closed, meaning they wrap around while still maintaining geometric flatness. And it can get weirder. A Möbius strip is just a cylinder with a rotation made before the ends connect up. A Klein bottle is just a donut with a rotation. A cylinder, a donut, a Möbius strip, and a Klein bottle are all geometrically flat.

In three dimensions, there are 17 known distinct topologies that are all geometrically flat. My favorite being, of course, Hantzsche-Wendt space, which involves hexagonal tilings of the same pattern.

Searching for the universe’s shape

We’ve searched for closed topologies. We’ve looked for intersection points in the cosmic microwave background, or galaxies that appear on opposite sides of the sky. As far as we can tell, the universe is both flat and simple, meaning none of the dimensions wrap around on themselves. But again, there’s a limit to what we can see, so we may never know for sure.

And I haven’t even gotten started on the multiverse, where our universe, even beyond the observable limit, is just one bubble amongst a potential infinity of other bubbles, all expanding away from each other and spawning new big bangs in the spaces between, but… I think that’s enough for today.

Adapted from an article originally published in UniverseToday.

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