In the first moments after the Big Bang, the Universe was a hot soup of particles. Among them floated superheavy neutrinos — thousands of times more massive than their light counterparts that permeate us today. Their masses were almost identical, like triplets rather than random passersby.

This picture was painted by a mathematical symmetry — the unusual modular group A₄. It rigidly ties particle masses together, leaving no freedom for fine-tuning. As a result, the superheavy neutrinos end up nearly degenerate in mass (differing by fractions of a percent). It's like three weights cast from the same mold. Their decays in the early Universe produced a tiny excess of matter over antimatter — the very excess that makes our existence possible.

But this elegant picture has a cosmological shadow. As the Universe cooled, it underwent a phase transition, like water freezing into ice. The field responsible for the symmetry 'froze' differently in different regions of space, and domain walls grew between them. Such a fence of energy would have come to dominate the Universe, yet we don't see it.

The authors found an elegant way out: the same superheavy neutrinos create a tiny pressure imbalance on the walls. The walls start to move, collide, and disappear, generating ripples in spacetime — gravitational waves. Their spectrum is unusual: two peaks separated by many octaves. One comes from the wall collisions, the other from the phase transition itself. Together, they resemble a double bell strike, from which one can reconstruct the mass of the invisible clapper.

Future detectors, the space observatory LISA and the ground-based Einstein Telescope, will be able to hear both peaks. This is a rare chance to peer into the epoch when particle masses were formed and to indirectly weigh what will never be trapped in an accelerator.