In the first moments of its life, the universe resembled a boiling cauldron. Matter wasn't spread evenly — clumps and voids were brewing within it, and their violent motion gave rise to a trembling of space itself: gravitational waves. Today, we try to catch their echoes (for instance, with the NANOGrav network of radio telescopes) and compare them with predictions. To do this, physicists run numerical simulations on supercomputers, recreating that ancient storm.

But there's a catch. When you compute the spectrum directly from the simulation, the distribution of wave energy across frequencies, a fine jitter appears at low frequencies. It looks like ripples that were never expected. The cause isn't physics but mathematics: when averaging squared amplitudes, doubled frequencies sneak into the signal. It's as if an echo bounced off a wall and superimposed on itself. The authors call these 'parasitic wiggles' and show that they have nothing to do with real waves. Such a spectrum cannot be shown to observers: it's misleading.

The solution came from a simple idea: let the simulation 'cool down.' When the source of waves — for example, a network of domain walls (hypothetical folds in spacetime)—disappears, the waves continue to roam the universe for a while. If you extend the calculation for several Hubble times (periods of doubling of the universe's size) after the source is turned off, the parasitic oscillations smooth out by themselves. The physicists tested this with the CosmoLattice code, simulating exactly a network of domain walls. The extended simulation allowed them to recover the true, smooth infrared slope of the spectrum — the very one that carries the memory of the most violent stage of wave birth.

The authors warn: artificially stretching the equations using the well-known Press–Riddick–Spergel (PRS) trick won't work here. It gives incorrect spectra, even if you carefully renormalize the sources. Only an honest physical continuation of the calculation, which took a few extra Hubble times, brings the true signal to light. The method is quite universal and applicable to any numerical model of hypothetical gravitational wave sources in the early universe.