On the gravitational wave production from the decay of the Standard Model Higgs field after inflation

During or towards the end of inflation, the Standard Model (SM) Higgs forms a condensate with a large amplitude. Following inflation, the condensate oscillates, decaying non-perturbatively into the rest of the SM species. The resulting out-of-equilibrium dynamics converts a fraction of the energy available into gravitational waves (GW). We study this process using classical lattice simulations in an expanding box, following the energetically dominant electroweak gauge bosons $W^\pm$ and $Z$. We characterize the GW spectrum as a function of the running couplings, Higgs initial amplitude, and post-inflationary expansion rate. As long as the SM is decoupled from the inflationary sector, the generation of this background is universally expected, independently of the nature of inflation. Our study demonstrates the efficiency of GW emission by gauge fields undergoing parametric resonance. The initial energy of the Higgs condensate represents however, only a tiny fraction of the inflationary energy. Consequently, the resulting background is very suppressed, with an amplitude $h^2 \Omega_{\rm GW}^{(o)} \lesssim 10^{-29}$ today. The amplitude can be boosted to $h^2 \Omega_{\rm GW}^{(o)} \lesssim 10^{-16}$, if following inflation the universe undergoes a kination-domination stage; however the background is shifted in this case to high frequencies $f_p \lesssim 10^{11} {\rm Hz}$. In all cases the signal is out of the range of current or planned GW detectors. This background will therefore remain, most likely, as a curiosity of the SM.