There are slight variations in the CMB: Some spots on the last scattering surface (where the CMB photons originated) are a bit warmer than average, while others are a bit cooler. These patterns were created by sound waves propagating through the plasma of the early universe. The waves themselves were triggered by minute quantum fluctuations in the fabric of space as it rapidly expanded during the first moments of the Big Bang, not unlike the waves that might be created if rocks of various sizes were dropped randomly into a pond. The crests of the waves would correspond to places of slightly elevated temperature or density, whereas troughs would signify places of depressed temperature or density.
This pattern is imprinted in the CMB. However, you can’t just look at a CMB map and see waves leaping off the page. You need to make a detailed examination of statistical correlations in order to measure the size distribution of troughs and crests. It’s like analyzing a scratchy recording of Beethoven’s Ninth Symphony to reconstruct the original sheet music and see what notes the universe was playing at its birth. “A piccolo and a tuba are both wind instruments, but you can easily hear the difference because of the notes they produce,” said Craig Copi, a Compact team member at Case Western.
How might identifying those notes help? A universe with a particular topology may amplify some notes and muffle others. Consider, for instance, a puzzling feature of the CMB. Imagine you have two telescopes. One points straight up. The other is 10 degrees off. Statistically, if you measure the temperature of the CMB at both locations, the results will be correlated. If one spot is warmer than average, the other is also likely to be warmer than average. Other angles will show an anticorrelation — one spot warm, the other cold.
These relationships hold for all angles between zero and 60 degrees. “But above 60 [degrees], there is no correlation, and we have no explanation for that,” Copi said.
Topology might be the answer. If you have a taut string of a certain length and you pluck it, the notes it can make will have a maximum wavelength, meaning there are low notes it simply cannot produce. Correlations in the CMB above 60 degrees would likely be caused by long-wavelength fluctuations, but large-angle correlations of that magnitude have not been seen. “Maybe our drum [universe] doesn’t produce those notes [because] topology would naturally cut off that scale,” Copi suggested. In other words, maybe we live in a piccolo rather than a tuba.
So how do we find out? The first step is to map out the sounds that we expect to be produced by the various topologies.
Possible Topologies
Compact researchers have started with the easiest topologies — the 17 different flat spaces, starting with a simple 3D torus, labeled E1, and proceeding through more complicated configurations up to E17.
A Compact collaboration paper, published last year, presented the templates for the nine flat topologies that are called “orientable,” which means that if you are on such a surface and you’re pointing upward, and you travel around in a loop, you’ll still be pointing up when you return to your starting point. A paper with templates for the remaining eight nonorientable flat topologies should become available early this year. A nonorientable surface (such as a Möbius strip) has a built-in twist; upon completing a loop around such a space, you’ll change your orientation from right side up to upside down (or vice versa).
Akrami and his doctoral student are starting the next phase, working on the signatures of topologies with positive curvature, like a sphere. There are five general classes of these topologies.
The Compact team is also exploring how to study the topology of the universe not just with the CMB, but also by using the distribution of galaxies across the universe. Whereas the CMB provides just 2D data — a sort of cross section of the universe — galaxies fill the entire 3D volume of space, providing far more data points to analyze. Compact members are hoping that improved maps of the galaxy distribution due to come in over the next several years from the Euclid, Roman and Spherex space telescopes can enhance the search for cosmic topology.
Cornish views Compact as a “low-probability, high-reward” proposition. “If I had to bet, I don’t think they’re going to find anything,” he said. “But the question is so important,” he added, that it ought to be explored “to the fullest extent.”
Starkman doesn’t believe that anyone can assess the probability of success or failure just yet. “When it comes to the topology of the universe, we simply have no idea what to expect,” he said. He is motivated to carry on, in part, because topology can potentially explain the anomalies in the CMB — not only the apparent 60-degree cutoff in its statistical correlations, but also the perplexing differences in the patterns observed above and below the orbital plane of the solar system (called the North-South asymmetry). Starkman can’t say for sure that these anomalies are due to topology, but he has yet to hear any other convincing explanation.
These confounding patterns, Cornish acknowledged, could be “caused by the universe having a particular shape,” or they could be due to “a random fluke.”
Compact investigators have found that the data that’s accumulated over recent decades has strengthened the case for the physical reality of these anomalies rather than weakening it, and time will tell whether that trend continues. The group intends to carry out its work over the next five to 10 years, Akrami said. “We’ll either find the topology of the universe,” he said, or determine that “the universe is so big that its topology cannot be detected” — at least with the tools available to us now.
Some may find the latter outcome disappointing, if it comes to pass. After all that effort, we’d surely know a lot more than Aristotle ever did. But we’d still lack an answer to the question he deemed “all-important to our search for the truth.”
1: David Spergel is now the president of the Simons Foundation, which funds this editorially independent magazine. Simons Foundation affiliations have no influence on our coverage. For more information about our editorial independence and our relationship to the Simons Foundation, please see our About page. (Return to article.)
Correction: January 27, 2025
An earlier version of this article misspelled Mark Kac’s name.