The simplest assumption is that there is far more universe beyond our cosmic horizon: more stars, more galaxies and, naturally, more AI-generated cat videos. It is like standing somewhere on Earth and assuming the planet continues beyond the visible horizon.

But how large is the universe as a whole, including everything we cannot see?

The frustrating answer is that we may never know.

The Observable Universe Has a Fundamental Limit

The boundary of the observable universe is not simply the farthest distance current telescopes can reach. It reflects deeper limits on the information that can ever arrive here. Even if we waited for an arbitrarily long time, only a finite amount of information would become accessible to us.

Beyond that boundary, we are left with observations, mathematical models and educated guesses.

One possibility is straightforward: the universe is infinite. It continues forever without an endpoint.

Another possibility is that the universe is finite.

That raises an obvious question: can something be finite without having an edge?

Earth provides the answer.

How Earth Shows That a Finite Space Can Have No Edge

Earth’s surface has a finite area, but someone traveling across it would never suddenly reach a boundary where the ground ends. Leaving Earth’s surface and heading into space would involve a third dimension, but that is beside the point. The two-dimensional surface itself is finite and curved, yet it has no edge.

How Geometry Reveals Curvature

We do not have to leave Earth to demonstrate that its surface is curved. Mathematics provides several ways to detect curvature while remaining entirely on the surface.

Consider a triangle. On a perfectly flat plane, its three interior angles add up to 180 degrees. Thank you, Euclid.

Now imagine drawing the shortest paths between three widely separated cities on Earth. The resulting triangle will not behave exactly like one drawn on paper. Because the surface beneath it is curved, its interior angles can add up to more than 180 degrees.

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

Imagine that you and I start at different points along the equator and travel due 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 use similar geometric tests to investigate the shape of the universe.

How Ancient Light Tests the Shape of the Universe

One of the most powerful tools is 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, which allows them to predict the patterns that should appear in this ancient glow.

Those predictions include tiny temperature fluctuations scattered throughout the CMB—and astronomers observe them.

More importantly, scientists can calculate how large these temperature patches should appear. If space is strongly curved, light traveling toward us across billions of light-years will follow altered paths. That distortion changes the apparent size of the patterns.

Astronomers can therefore compare the observed size of CMB features with the sizes predicted by different models of cosmic geometry.

The features appear at the expected scale for an essentially flat universe.

This is why scientists say the observable universe appears geometrically flat.

But has the mystery been solved? Does a flat universe automatically mean an infinite universe?

Not completely.

Why a Flat Universe May Still Be Finite

Imagine trying to measure Earth’s curvature from your neighborhood. The area would appear mostly flat. Small triangles would behave almost exactly as Euclid predicted, and short parallel paths would not visibly converge.

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

The same idea may apply to space.

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

It is possible that the universe has a curvature that becomes noticeable only at scales much larger than those we can observe. Tens of billions of light-years may sound enormous, but they could still represent only a small portion of the entire universe.

If space eventually curves back around itself, traveling continuously in one direction could, in principle, bring you back to your starting point—just as traveling around Earth eventually returns you to where you began.

In reality, this remains a theoretical thought experiment. The expansion of the universe means that regions beyond our cosmic horizon will remain permanently out of reach.

But the possibilities become even stranger.

Can a Flat Universe Wrap Around Itself?

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

To see how, imagine a flat sheet of paper. Draw a triangle and several parallel lines on it. Then, without stretching or tearing the paper, bend it into a cylinder.

Locally, the geometry remains flat. Triangles still behave like ordinary triangles, and parallel lines remain parallel. But one direction now loops around and connects back to itself.

This illustrates the difference between geometry and topology.

Geometry describes properties such as curvature. Topology describes the broader ways in which a space is connected.

The observable universe appears geometrically flat. That observation does not automatically reveal whether one or more dimensions remain locally flat while wrapping around and connecting back to themselves.

Cosmic Topology Could Be Stranger Than It Looks

Mathematics allows some unusual possibilities. A Möbius strip can be created by connecting the ends of a strip after adding a twist. A Klein bottle is another example of an unusual connected surface. Cylinders, doughnuts, Möbius strips and Klein bottles show how a space can have a locally familiar shape while possessing a very different overall structure.

In three dimensions, mathematicians have identified 17 different topologies that can remain geometrically flat. One particularly interesting example is the Hantsche-Wendt space, which contains repeating structures related to hexagonal patterns.

Scientists Have Searched for Signs That the Universe Loops

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

One strategy is to search for repeating patterns in the cosmic microwave background. Another is to look for galaxies appearing in different parts of the sky because their light has traveled around a connected universe.

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

Based on everything we can currently observe, the universe appears to be geometrically flat and topologically simple. In other words, no evidence has been detected that a dimension loops back and reconnects.

But our cosmic horizon imposes fundamental limits. If a loop is larger than the observable universe, we may have no way to detect it.

Will We Ever Know Whether the Universe Is Infinite?

We may never know for certain whether the universe as a whole is infinite, finite, curved or connected in some vast and unfamiliar way.

And then there is the multiverse.

According to some cosmological ideas, everything we call the universe—including regions far beyond the observable horizon—could be one bubble among potentially countless others. These bubbles may expand away from one another while new regions experience their own big-bang-like beginnings.

But that is probably enough cosmic geometry for one day.