Is the Universe Shaped Like a Donut? The Radical Search for Cosmic Topology
If you could board a spaceship capable of flying in a perfectly straight line forever, what would happen? Common sense says you’d travel through endless galaxies, never reaching an edge, never looping back. But common sense might be wrong. The universe could be finite — and if you flew far enough, you might eventually return to where you started, having circumnavigated all of existence like a cosmic Magellan. The question of whether the universe wraps back on itself — its topology — is one of the deepest and most persistently overlooked questions in cosmology. Now, a comprehensive review from the COMPACT Collaboration, invited for publication in Nature Astronomy, lays out everything we know, everything we don’t, and the astonishing possibility that the evidence may already be hiding in data we’ve already collected.
Background & Context
Most people — and, until recently, most cosmologists — have assumed that the shape of the universe is determined entirely by its curvature. If space is positively curved, like the surface of a sphere, the universe must be finite. If it’s flat or negatively curved, it must be infinite. This intuition is wrong. Topology and geometry are different things. You can take a flat sheet of paper and roll it into a cylinder, and then connect the ends to make a torus — a donut. The local geometry hasn’t changed: every point on that donut still feels perfectly flat. But the global structure is now radically different. Travel far enough in one direction and you loop back to your starting point.
This is the central insight behind cosmic topology: the universe could have the flat, Euclidean geometry that our best measurements strongly favour, yet still be finite and closed, its space wrapping back on itself through hidden connections. The mathematical possibilities are surprisingly rich. For flat three-dimensional space alone, there are exactly 18 possible topologies — not infinite, not one, but eighteen. For positively curved and negatively curved geometries, the possibilities are far more numerous. The paper, led by Craig Copi, Deyan Mihaylov, Anna Negro, and Glenn Starkman of the COMPACT Collaboration, provides the most thorough synthesis to date of the decades-long effort to determine which of these possibilities, if any, describes our actual universe.
What the Researchers Did
The COMPACT team’s review synthesises three decades of observational campaigns, from the COBE satellite of the early 1990s through WMAP and Planck, and looks ahead to next-generation experiments. The primary tool for this search has been the cosmic microwave background (CMB) — the faint afterglow of the Big Bang, whose light has been travelling toward us for 13.8 billion years. If the universe is topologically non-trivial, meaning it has “unshrinkable closed loops” — paths that, if you travelled far enough along them, would bring you back to your starting point — then the CMB should carry subtle but distinctive fingerprints.
The most intuitive method is the “circles in the sky” search. If space wraps around, light from the same region of the early universe could reach us along two different paths, creating matching circles of temperature patterns on opposite sides of the sky. The WMAP and Planck teams conducted exhaustive searches for such matched circles. They found none — but that doesn’t mean the topology is trivial. It only means that if there are closed loops passing through our location, they must be larger than the diameter of the last scattering surface, the spherical shell from which the CMB originates.
A more powerful technique, developed in recent years, uses full Bayesian likelihood analysis. Rather than looking for individual matching circles, this approach computes the statistical signature that a given topology would imprint on the entire pattern of CMB temperature fluctuations. In a universe with non-trivial topology, the correlations between different directions on the sky lose their clean diagonal structure. The correlation matrix — the mathematical object that encodes how temperature fluctuations in different directions are related — becomes richly patterned with off-diagonal entries. The Planck team applied this method to a limited set of Euclidean topologies and found no signal — but critically, the COMPACT review emphasises that this was far from exhaustive. They only looked at a fraction of the possible topologies, and only a fraction of the possible observer positions within them.
What They Found
Here is where the story gets genuinely exciting. The COMPACT team’s recent work shows that cosmic topology might be detectable even when the topology scale is larger than the visible universe. Using the Kullback-Leibler divergence — a measure of how distinguishable two probability distributions are — they demonstrated that the statistical fingerprint of topology can remain above the detectability threshold for manifolds in which the shortest closed loop through the observer measures up to approximately 1.3 times the diameter of the last scattering surface.
This is a dramatic finding. The conventional wisdom had been that if the universe’s topology scale exceeds the distance to the CMB, we simply cannot see it. The COMPACT results overturn that assumption. Topology breaks statistical isotropy — the principle that the universe looks the same in all directions — and this broken symmetry propagates through the correlation structure in ways that can be detected even when individual matched circles are invisible.
Moreover, the shortest closed loop through us may not be the shortest closed loop in the universe. Because topology generically breaks homogeneity as well as isotropy, some regions of space could have shorter loops than the one that passes through our location. In orientable Euclidean manifolds, the shortest loop anywhere can be up to six times shorter than our local loop — meaning the universe could be significantly more constrained than we think, and the topological signal significantly stronger elsewhere.
Why It Matters
Determining the topology of the universe is arguably the most fundamental question in cosmology. It’s not an incremental refinement of parameters we already know — it would tell us whether the universe is finite or infinite, whether its total volume has a definite number we could calculate, and whether the laws of physics operate on a closed, bounded stage or an unbounded one. This has profound implications for the arrow of time, the nature of quantum fields, and even the question of whether the universe had a beginning in any meaningful sense.
There’s also a tantalising connection to some of cosmology’s most stubborn puzzles. The CMB exhibits several well-documented “anomalies” — unexpected alignments of temperature fluctuations, an absence of correlations on the largest angular scales, and a hemispherical power asymmetry between opposite sides of the sky. While none of these individually rises to the level of a discovery, their collective persistence across multiple experiments is striking. A non-trivial cosmic topology could provide a unified explanation for several of these anomalies, particularly the lack of large-scale correlations, which the Poincaré dodecahedral space model was famously proposed to explain in 2003.
How It Could Change Our Lives
A discovery of cosmic topology would be — to understate it considerably — one of the greatest scientific revelations in human history. It would mean that the total volume of the universe is finite and, in principle, calculable. It could mean that the light from distant galaxies has already looped around multiple times, and that with sufficiently powerful instruments we might someday see multiple images of the same galaxy at different epochs in its evolution. It could resolve whether certain quantum gravitational effects — such as the Casimir-like backreaction of topology on cosmic expansion — have played a role in the early universe’s evolution.
More concretely, the search for cosmic topology is about to enter a golden age. The LiteBIRD satellite, a Japanese-led mission scheduled for launch in the early 2030s, will measure CMB polarisation with a sensitivity that far surpasses Planck, particularly at the large angular scales where topological signals concentrate. The Taurus balloon experiment aims to map E-mode polarisation across 70% of the sky at precisely the multipole range where the topology-induced signal is strongest. Meanwhile, next-generation galaxy surveys and line-intensity mapping experiments will probe the three-dimensional distribution of matter throughout the observable volume, offering orders of magnitude more independent data points than the two-dimensional CMB alone can provide.
The Bigger Picture
The topology question sits at a rare intersection in modern physics. It connects the largest observable scales — the entire cosmic microwave background — to the smallest, where quantum gravity effects might imprint themselves on the global structure of spacetime. The COMPACT review discusses how cosmic topology interfaces with quantum cosmology, including the Hartle-Hawking no-boundary proposal, the cobordism conjecture from string theory, and recent work on how topology-induced Casimir effects could transmit isotropy violations from the Planck scale to cosmological observables. In other words, measuring the shape of the universe might, remarkably, give us experimental traction on quantum gravity — the holy grail of theoretical physics.
Limitations & What’s Next
The hard truth is that we may never know the topology of the universe. If the topology scale is vastly larger than the visible universe — if our fundamental domain is, say, a thousand times the size of the observable region — then no conceivable experiment will ever detect it. The COMPACT authors are candid about this: their paper is not a promise of discovery but an argument for the importance of looking. The monumental nature of a positive detection, they argue, compels us to search as carefully as possible with every dataset we have and every dataset we will collect. The search is underway, and the universe may yet turn out to be stranger — and more finite — than we ever imagined.
📄 Source: Copi, C.J., Mihaylov, D.P., Negro, A., Samandar, A., Starkman, G.D., et al. (COMPACT Collaboration). “The Topology of the Universe.” Invited Review for Nature Astronomy. arXiv:2606.24886, June 2026.