The merger of two neutron stars is like a strike on a gong: a ripple in space, a gravitational wave, spreads through the universe. Detectors on Earth catch this ripple and, from its strength, calculate the distance to the source. But the wave doesn't travel through a void: along the way, it is slightly bent by the gravitational fields of galaxy clusters. This is similar to how the light from a streetlamp shimmers when passing through wet glass. Astronomers call this distortion weak lensing.

Usually, this distortion is a nuisance for precise distance measurements. But the authors of the new study propose not to discard it, but to use it as a tool. If we catch hundreds of signals from neutron star mergers, the tiny distortions in each signal can reveal how unevenly matter is distributed in the universe. This unevenness is quantified by the number sigma-8: the larger it is, the more strongly matter is clumped into structures — galaxies, clusters, filaments.

The future detector Einstein Telescope could measure sigma-8 with 10% precision if it registers 300 neutron star mergers with electromagnetic counterparts. The space-based detector LISA, which will catch waves from supermassive black holes, would give 30% precision from just 12 events. This would allow us to test how dark matter influences the growth of structures and compare it with what we see in ordinary light from galaxies.

Thus, the tremor from distant catastrophes becomes a ruler for measuring the invisible part of the universe.