Fixing IR tail of gravitational waves from domain walls

Numerical simulations of gravitational waves (GW) production during violent evolution of matter inhomogeneities in the early Universe yield highly wiggle infrared parts of the spectra. Obtained directly from the two-point correlation function, these wiggles are nonphysical, corresponding to the parasitic, double frequency terms in naively averaged squared oscillation amplitudes of GW, and hence must be washed out. The deep infrared behavior can be predicted on general grounds, e.g. fixed by causality considerations. However, what matters for real observations, e.g. like that of NANOGrav, and what can be only inferred from numerical simulations, is the infrared slope near the maximum of the spectrum. It reflects the dynamics responsible for the GW production in its heyday, and hence must be accurately predicted. We illustrate the problem with numerical simulations of the Domain Wall network performed with the help of code CosmoLattice. We suggest a numerical procedure to smooth out these parasitic wiggles, which allows us to recover the true spectrum. Being quite generic, it may be applied to numerical simulations of other hypothetical sources of GW possibly operating in the early Universe. The procedure requires to extend the simulation by a few Hubble times after termination of the GW production. We checked with numerical simulations, that the technically natural long-time extension of simulations, which becomes available via artificial scaling of different parts in the scalar sector equations provided by PRS prescription, gives wrong GW spectra even if the source terms are properly rescaled.