Is the universe infinite? The answer gets weird fast

The simplest assumption is that beyond our cosmic horizon, there is simply more universe. More stars. More galaxies. More AI-generated cat videos. It is similar to standing somewhere on Earth and assuming that beyond your visible horizon, there is still more Earth.

But how large is the entire universe, including everything beyond what we can see?

The frustrating answer is that we may never know.

The Limits of the Observable Universe

The boundary of the observable universe is not merely the farthest distance our telescopes can currently reach. It represents a deeper limit on what information can ever reach us. The universe contains a finite amount of information that can become accessible to us, even if we waited for an arbitrarily long time.

Beyond that boundary, we are left to infer and speculate.

One possibility is straightforward: the universe is infinite. Space simply continues forever with no endpoint.

But another possibility is that the universe is finite.

That immediately raises an obvious question. How can something be finite without having an edge?

Earth provides the answer.

The surface of our planet has a finite area, yet someone traveling along that surface never encounters a boundary where the ground suddenly ends. Yes, Earth has an edge if you leave its surface in the third dimension and head into outer space, but that misses the point. The two-dimensional surface itself is finite and has no border because it curves back around.

How Geometry Reveals Curvature

We do not need to leave Earth to prove that its surface is curved. Mathematics gives us several ways to detect curvature while remaining entirely on the surface.

Triangles provide one example. On a perfectly flat plane, the three interior angles of a triangle add up to 180 degrees. Thank you, Euclid.

But imagine drawing enormous lines between three widely separated cities on Earth. The resulting triangle would not behave like one drawn on a sheet of paper. Its interior angles would add up to more than 180 degrees because the surface beneath it is curved.

Parallel lines offer another clue. On a flat plane, parallel lines never meet. On a curved surface, however, lines that begin parallel can eventually converge.

Imagine that you and I begin at different points along the equator and travel straight north. Eventually, our paths meet at the North Pole. Neither of us turned toward the other. The surface of Earth curved beneath us.

Astronomers can perform similar geometric tests on the universe itself.

Ancient Light Tests the Shape of Space

One of the most powerful tools comes from the cosmic microwave background, or CMB.

This ancient radiation was released when the early universe cooled enough for light to travel freely through what had previously been a hot, dense plasma. Scientists understand much of the relevant plasma physics (we have a decent understanding of plasmas here on Earth), which allows them to predict what patterns should appear in this ancient glow.

Those predictions include tiny temperature variations scattered across the CMB.

And those variations are exactly what astronomers observe.

More importantly, scientists can calculate how large those temperature patches should appear. If space were strongly curved, the light traveling toward us across billions of light years would follow altered paths. That distortion would change the apparent size of the patterns.

Astronomers can therefore compare the observed size of the CMB features with the size predicted for different cosmic geometries.

The features appear at essentially the expected scale for flat space.

That is why scientists say the universe appears to be geometrically flat.

So is the mystery solved? Does a flat universe automatically mean an infinite universe?

Not quite.

Flat Does Not Necessarily Mean Infinite

Imagine trying to measure the curvature of Earth while confined to your own neighborhood. The area would look nearly flat. Small triangles would behave almost exactly as Euclid predicted, and short parallel paths would not noticeably converge.

The problem would not be that Earth is actually flat. Your measuring area would simply be too small compared with the size of the planet.

Something similar could be true of the universe.

Our measurements are limited to the observable cosmos. Within that enormous region, space appears extremely flat. But the universe outside our observable patch could be vastly larger.

It is therefore possible that the universe has curvature that becomes apparent only on scales much larger than we can access (I know that tens of billions of light-years isn't exactly tiny, but it is compared to how big the universe COULD be.)

If so, space might eventually curve back around itself.

In principle, that could mean traveling continuously in one direction would eventually return you to where you started, much as traveling around Earth can bring you back to your starting point.

In practice, the expansion of the universe places regions beyond our cosmic horizon permanently out of reach, so such a journey remains a theoretical thought experiment.

But things can get even stranger.

The Universe Could Be Flat and Still Wrap Around

A universe can be geometrically flat without being infinite in every direction.

To understand how, picture a flat sheet of paper. Draw triangles and parallel lines on it. Now bend the paper into a cylinder without stretching or tearing it.

Locally, the geometry remains flat. The triangles still behave like ordinary triangles, and the parallel lines still behave like parallel lines. Yet one direction now loops around.

This highlights the difference between geometry and topology.

Geometry describes properties such as curvature. Topology describes the broader way a space is connected.

The observable universe appears geometrically flat. But that does not automatically tell us whether one or more dimensions might wrap around and connect back to themselves while remaining locally flat.

Topology allows for some very strange possibilities.

A Mobius strip can be created by connecting the ends of a strip after introducing a twist. A Klein bottle can be thought of as another unusual connected surface. Cylinders, donuts, Mobius strips, and Klein bottles can all illustrate how spaces with locally flat geometry can have very different overall structures.

In three dimensions, mathematicians have identified 17 distinct topologies that can all remain geometrically flat. One particularly interesting example is Hantzsche Wendt space, which involves repeating structures related to hexagonal patterns.

Scientists Have Looked for Cosmic Loops

Astronomers have searched for evidence that the universe has a closed topology.

One strategy is to look for repeated patterns in the cosmic microwave background. Another is to search for galaxies that might appear in different places on opposite sides of the sky because their light has traveled through a universe that wraps around itself.

So far, researchers have found no convincing evidence that this happens.

Based on everything we can currently observe, the universe appears both geometrically flat and topologically simple. In other words, there is no detected sign that its dimensions loop back on themselves.

But once again, our cosmic horizon creates a fundamental limitation. If the scale of any such looping is larger than the observable universe, we may never be able to detect it.

That means we may never know with certainty whether the entire universe is infinite, finite, curved, or connected in some larger and stranger way.

And then there is the multiverse.

In some cosmological ideas, everything we call the universe, including regions far beyond our observable horizon, might be only one bubble among potentially countless others. Those bubbles could expand away from one another while new regions undergo their own Big Bang-like beginnings.

But that is probably enough cosmic geometry for one day.