Across 750 million light-years, galaxy groups fall together as Newton predicts

Tiny imprints in the Big Bang's afterglow show pairs of galaxy groups drifting toward each other in the way an inverse-square law predicts, at distances never tested before. The measurement pins the exponent to within about 15%, not "almost exactly". It tests how gravity fades with distance, not how strong it is, and it does not settle whether dark matter or modified gravity explains the universe's missing mass.

13 October 2026 · How we rate evidence

The signal is a temperature difference of at most about a tenth of a millionth of a degree. It shows up in the cosmic microwave background, the afterglow of the Big Bang, where that light has passed through distant groups of galaxies. From it, a team using the Atacama Cosmology Telescope in Chile worked out how fast pairs of those groups, up to 750 million light-years apart, are falling toward each other.

On 24 August, ScienceDaily reposted a University of Pennsylvania release under the headline "Newton's 300-year-old law just passed its biggest test yet." It said gravity's strength "decreases with distance almost exactly as predicted by Newton's equations," and that the result "strengthens the case that dark matter is behind the universe's mysterious missing mass." The paper came out in Physical Review Letters on 15 April.

What they did. When a group of galaxies moves toward or away from us, its hot gas nudges the temperature of microwave light passing through it, slightly up or down. This is the kinematic Sunyaev-Zeldovich effect. For a single group the nudge is lost in noise. The team, led by Patricio Gallardo of Penn, instead measured 227,837 luminous red galaxies, each a marker of the group it sits in, and compared the microwave temperature around every pair. Pairs falling toward each other leave a small, consistent temperature difference. Averaged over hundreds of thousands of pairs, that difference gives the mean speed at which groups at a given separation are closing in, in 15 distance bins from 30 to 230 megaparsecs.

Then came the test. Using the measured clustering of 686,000 galaxies, which says how much matter surrounds a typical pair, they predicted how that closing speed should change with distance if the pull falls off as 1/rⁿ. Newton's law is n = 2. MOND, short for Modified Newtonian Dynamics, a theory that changes gravity at very weak pulls instead of adding dark matter, behaves in the authors' derivation like n = 1 at these distances. They let n float and fitted it to the data, so the data could have contradicted Newton.

What they found. The best fit is n = 2.1 ± 0.3, well within range of Newton's 2. At 95% confidence, n is above 1.4. With n fixed at 2, the formula fits the 15 data points well. With n fixed at 1, it fits poorly: a fit that bad would happen by chance about 4 times in 1,000. In the joint fit, n = 1 sits 3.3 sigma from the best estimate. For a standard two-sided test, that is about 1 chance in 1,000 of a fluctuation that large if n really were 1. A second way of writing the force law, in the paper's appendix, puts n above 1.8 at 95% confidence.

Direct tests of the force law at such distances had been lacking, the paper notes; earlier large-scale checks of gravity assumed a known history of cosmic expansion. The authors call it the largest-scale direct test of MOND to date; on scale, the headline is fair.

What it doesn't show. First, the release's "almost exactly" oversells the precision. An uncertainty of 0.3 on 2 is about 15%. The data rule out a 1/r law, but they still allow an exponent anywhere from about 1.4 to 2.7. Laboratory and Solar System tests of the inverse-square law are vastly more precise; this one reaches much farther, not closer.

Second, only the shape was tested, not the strength. How hard the groups pull depends on how much mass there is and on gravity's constant. In this measurement that overall size is tangled up with an unknown, how much electron-rich gas each group holds, so the team fitted it freely. The paper therefore says nothing about how much mass, dark or otherwise, is doing the pulling. The paper makes no claim about the amount of mass; the release's line about "the missing mass revealed by these observations" describes something the study didn't measure.

Third, the error bars are statistical. The paper leans on earlier checks of the telescope maps, and describes its modelling shortcuts, such as treating galaxy clustering as fixed over the redshift range, as small effects in words, without folding them into the uncertainty. It reports no blinding. Those two gaps are what keep our shape rating close to Early.

Fourth, whether this is a test of MOND is still open. The MOND prediction is a simplified version that leaves out a feature proponents call the external field effect, in which the pull of everything else in the universe changes how two objects attract. The authors say it "likely does not affect our analysis", since 30 megaparsecs dwarfs any cluster, though checking would need simulations. Yet by the paper's own description the effect depends on the strength of the surrounding pull, not on size.

What would have to be true. For gravity to be modified rather than dark matter to exist, the modified law would now have to fall off as an inverse square between 100 and 750 million light-years, at least roughly. MOND in the simple form tested here doesn't. Other theories can. In an unreviewed April preprint, the theorist John Moffat argued that his own modified-gravity theory, tuned to fit galaxy clusters, becomes inverse-square beyond about 5 megaparsecs, with a stronger overall pull that this test can't see. So the result narrows the options for modified gravity; it doesn't choose dark matter over all of them.

One smaller fix. The release says the team examined "hundreds of thousands of galaxy clusters"; it measured galaxies, each standing in for its group or cluster.

Why it's still interesting. Gravity's distance law had never been checked directly on scales this large, and it held. The method is new: rather than assuming a theory of how structure grows, it reads the pull straight from how galaxy groups move and cluster. It will improve fast. The authors estimate that about 4 million galaxies from surveys such as DESI, with maps from the Simons Observatory, could exclude a 1/r law at 10 sigma. We couldn't reproduce that figure; the simple scaling they cite gives about 14. And if the strength of the pull can be measured too, the same method could weigh the matter doing the pulling.

Open questions.

Does the exponent hold up with different data? A separate team using a different telescope, such as the South Pole Telescope or the Simons Observatory, with galaxies from DESI, and with analysis choices fixed in advance, would show whether n ≈ 2 is a property of gravity or of this dataset. At ±0.1 precision the test would start to probe theories between 1/r and 1/r², not just the extremes.

What does full MOND predict here? Simulations of pairwise motions under MOND, including the external field effect, would say whether MOND really predicts 1/r at these distances or something steeper. If it's steeper, this result says little about MOND. If 1/r holds, the paper's verdict stands on firmer ground.

How strong is the pull? An independent measure of how much gas each group holds, from other microwave signals or from radio bursts whose signals are slowed by that gas, would turn the fitted overall size into a measurement. That, not the shape, is what separates dark matter from inverse-square modified gravity with a stronger pull.

A note on timing. The paper and its arXiv version appeared on 15 April 2026, with news coverage within days. ScienceDaily's repost came on 24 August, about four months later. The science didn't change in between.