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In 2015, detectors caught a gravitational wave for the first time — a ripple in space that traveled from merging black holes. Since then, such signals have become a new window into the universe for astrophysics. But gravitational waves can do more: they carry the imprint of the very theory of gravity. If Einstein's theory is not quite accurate, then waves from distant catastrophes might sound slightly different than general relativity predicts.

The authors of the study took one such alternative, so-called f(Q) gravity. In this theory, gravity arises not from the curvature of space but from its non-metricity — in other words, from the fact that under parallel transport, vectors can change their length. On the scales of the universe's expansion, this model behaves just like the standard cosmological model with dark matter and dark energy, but differences should show up in gravitational waves.

The scientists modeled how two future giants would register such waves: the European underground detector 'Einstein Telescope' and the American 'Cosmic Explorer.' Their sensitivity will be tens of times higher than that of current LIGO and Virgo. The calculations showed that both instruments will be able to tightly constrain the model's free parameter, even if the source is at a huge distance — up to a redshift of 5, when the universe was less than a billion years old. The slightest deviation from the Einsteinian waveform will become noticeable.

In this way, gravitational waves turn into a testbed for fundamental physics. The faint ringing of distant black holes will tell us not only what happened a billion years ago, but also the rules by which space itself operates.