We thought we knew the shape of the universe. We were wrong

Cosmologists have an embarrassing problem: we don’t know what shape the universe is. The cosmos has three possible geometries—positively curved like a sphere, flat like an infinite plane or negatively curved like a saddle—but geometry alone doesn’t determine shape. A flat universe could still wrap around in any number of ways.

It could be finite, infinite, or even folded back on itself like a Klein bottle someone left in the dryer. Einstein’s general theory of relativity describes local curvature brilliantly. (“Spacetime tells matter how to move; matter tells spacetime how to curve,” relativity pioneer John Wheeler quipped).

But Einstein’s greatest theory is essentially silent on the universe’s global topology. It’s one thing to sketch dragons on the blank edges of a map, but it’s another thing entirely not to even know where the edge is. Our touchstone for settling the question is the cosmic microwave background (CMB).

This is the faint thermal afterglow from some 380,000 years after the big bang that was unleashed when the hot, foglike plasma that filled the early universe cooled and cleared as primordial atomic nuclei bonded with free electrons. Missions such as the European Space Agency’s Planck space observatory have mapped this ancient signal with extraordinary precision. The most legible postulated signature of a topologically nontrivial universe (meaning one that doesn’t extend forever in all directions) would be pairs of circles on the CMB sky with precisely matching temperature patterns: finding an identical ring of hot and cold patches in two different directions could mean we’re looking at the same region of space from two different vantage points.

This would be as close as we’d come to the cosmos handing us a receipt for the same location, stamped twice. On supporting science journalism If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

After decades of fruitless searching, the failure to find these matching circles in the CMB produced a conclusion that calcified into consensus: any nontrivial topology must repeat at scales larger than the observable universe, or else it simply doesn’t exist. That is, according to Planck’s best all-sky CMB maps, either the universe is flatly infinite or it’s so nearly infinite that the distinction doesn’t matter. The logic was clean, the boundaries felt solid, and nobody had much cause to push on them.

But in science, tidiness is always a mild red flag. Now cosmologists in the international Collaboration for Observations, Models and Predictions of Anomalies and Cosmic Topology (COMPACT) have pushed, and the tidy picture is cracking. Their result: the observational constraints on a certain class of well-defined possible cosmic shapes are substantially weaker than everybody assumed.

Topologies once thought to be ruled out by Planck data are quietly back on the table. The reason this matters is beyond any mere pleasure of mapmaking: accurate cosmic topology would guide us to better theories of quantum gravity and could change how we think about the universe’s deepest past and furthest future. The proliferation of cosmic shapes suddenly resurrected by COMPACT should inspire awe—and no shortage of humility—because they collectively suggest there may be different physics, different histories and different answers to questions we’re not even asking yet.

Every time we mistake a provisional boundary for a permanent one, we foreclose possibilities that may turn out to be real. The schism runs through a deceptively simple assumption. The old reasoning held that the universe looping back on itself would necessarily intersect our line of sight if it were smaller than the distance to the spacetime origin of the CMB (which lies many billions of light-years away).

But loops don’t owe us that. A loop can thread through space in an orientation that completely misses the observer, producing no detectable circles on the CMB—and this unlucky arrangement can occur even when a loop’s size should place it well within our presumptive thresholds for detection. The COMPACT team found that the real minimum loop size can be two to six times smaller than what cosmologists had been treating as a hard lower bound.

In other words, we were expecting the mirror to be in front of us—but we forgot to check to our sides or the question of whether it might be tilted away entirely. The implications cascade. What looked like a narrow corridor of cosmic architectures now opens into an embarrassment of possibilities.

Many nontrivial topologies—universal shapes tossed to the “ruled out” pile with false confidence—now require a fresh look. The observable universe is no longer the aggressive arbiter of topology we thought it was, and the task of discerning the cosmos’s true form now appears far more difficult. That’s because the same geometry (what we learn from general relativity) can be stitched together in radically different ways—and there could be an infinite number of ways the universe could curl up on itself.

Even for flat spacetimes (like the one we suspect we live in), there are 18 possibilities. Eighteen! Cylinders, doughnuts, Klein bottles, and more are all topologically flat, it turns out.

Need proof? Draw two parallel lines on a flat sheet of paper. They stay parallel—that’s the definition of flatness.

Now roll the paper up. The lines stay parallel. Still flat.

All these topologies share the same geometry, which means general relativity treats them exactly the same. But they would manifest as different kinds of repeated patterns in different regions of the CMB sky. So it’s not just that we may be looking in the wrong places, and in the wrong ways, for a mirror reflecting cosmic shape; it’s that the CMB sky itself may be a hall of mirrors in which we aimlessly wander, chasing our own shadows.

What the COMPACT result clarifies, with some bluntness, is that we were reading our own assumption in the data. We assumed loops would intersect the observer and concluded they must be large because we didn’t see them. The loops were never required to cooperate.

This is the kind of error that looks obvious in retrospect and invisible until someone decides to check. Moving forward may require going beyond the twinned-circles method entirely—or at least supplementing it with a more sophisticated and statistically robust search for even subtler CMB-based signatures of cosmic shape. For now, the universe’s shape remains unknown.

The constraints are looser than advertised. The map still has a dragon problem—we just now know a little better what we’re missing.