Astronomers turn geometry into a cosmic ruler to test the shape of the Universe

In astronomy, where distances are too vast to measure with an ordinary ruler, geometry has long been the workhorse. Now, a new study has turned that ancient mathematical language into a precision tool to test the structure of the Universe itself¹.

Using faint distortions in the light from distant galaxies, an international team led by Divya Rana of Leiden University and Surhud More of the Inter-University Centre for Astronomy and Astrophysics has devised a way to isolate the geometry of the cosmos — almost as if peeling away its messy physical layers to expose its underlying shape.

“At its core, this is a geometric test,” Rana said. “We’re asking a simple question: how does distance scale in the Universe? But answering it requires removing a lot of astrophysical complications.”

The problem with cosmic maps

Modern cosmology relies heavily on a subtle effect called weak gravitational lensing. As light from distant “background” galaxies travels toward Earth, it is gently deflected by the gravity of nearer “foreground” galaxies. The result is a barely perceptible stretching of galaxy images — tiny distortions that, when measured across millions of objects, reveal the distribution of matter in the Universe.

Most of that matter is invisible. Dark matter, which neither emits nor absorbs light, reveals itself only through these gravitational fingerprints.

But there is a catch. To turn these distortions into a map of the cosmos, astronomers must know how far away each galaxy is. That distance is inferred through redshift — a shift of light toward longer, redder wavelengths as the Universe expands, which astronomers use as a measure of distance.

Precise redshift measurements require spectroscopy, which is slow and resource-intensive. So astronomers often rely on a shortcut: estimating redshift from a galaxy’s colour. These “photometric redshifts” are faster, but imperfect.

“Even small biases in redshift can ripple through the analysis,” More explained. “They affect how we infer distances, and therefore the geometry of the Universe itself.”

A trick of ratios

The new method sidesteps this problem with an elegant idea rooted in geometry.

Instead of measuring lensing distortions for one set of galaxies, the researchers compared how the same foreground galaxies distort multiple sets of background galaxies at different redshifts. By taking ratios of these distortions — what they call shear ratios — the team effectively cancels out much of the messy astrophysics.

“The beauty of ratios is that many uncertainties just drop out,” said Rana. “Things like galaxy formation physics or small-scale structure don’t matter as much anymore.”

What remains is a quantity that depends primarily on distances between observer, lens, and source galaxies. In simple terms, it focuses only on how far things are from each other, rather than how complicated the galaxies themselves are.

In technical terms, the ratio isolates the lensing efficiency, governed by angular diameter distances between objects. These are a way astronomers describe distances in an expanding Universe, based on how large objects appear in the sky. Because these distances depend on the expansion history of the Universe, the method acts as a kind of cosmic ruler.

Crucially, it also exposes errors in redshift estimates. If the assumed distances are off, the ratios will not match the expected geometric pattern.

Putting geometry to the test in space

To try out their approach, the team turned to data from the Hyper Suprime-Cam survey, one of the deepest wide-field imaging projects ever conducted. The survey maps hundreds of millions of galaxies, providing a rich dataset for weak lensing studies.

By dividing galaxies into multiple redshift bins and measuring shear ratios across them, the researchers were able to calibrate redshift biases with high statistical precision — meaning they could detect and correct even very small errors with high confidence — achieving signal-to-noise ratios exceeding 70 in some cases.

They then folded these corrections into cosmological models, refining estimates of key parameters such as the matter density of the Universe and the amplitude of cosmic structure.

The results aligned closely with independent measurements, suggesting the method is both robust and reliable.

“What’s exciting is that this gives us an independent cross-check,” More said. “We’re not relying on the same assumptions as traditional analyses.”

A tool for the next generation

In the coming years, a new generation of observatories, including the Vera C. Rubin Observatory, NASA’s Roman Space Telescope, and the European Space Agency’s Euclid mission, will map the Universe with unprecedented detail.

These surveys aim to tackle one of cosmology’s deepest mysteries — the nature of dark energy, the unknown force driving the accelerated expansion of the Universe.

Their success hinges on controlling systematic uncertainties, especially those tied to redshift estimation.

“Redshift errors are expected to be one of the dominant sources of uncertainty,” Rana said. “Our method provides a way to keep those errors in check.”

By turning geometry into a diagnostic tool, the shear-ratio technique may help ensure that the next decade of cosmology rests on firmer ground, he said.

There is something almost poetic in the approach. Geometry — one of the oldest branches of mathematics, once used to measure land and build pyramids — is now being used to probe the largest structure imaginable.

In stripping away the complexities of galaxy formation and focusing on pure relationships of distance and angle, the researchers have returned cosmology to a simpler foundation.

“The Universe is complicated,” More said. “But sometimes, if you look at it the right way, the underlying structure is surprisingly clean.”