  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.
