Gravitational Waves from Higgs Preheating after Inflaton $Z_2$-Symmetry Breaking

In this paper, nonperturbative lattice simulations are used to study Higgs preheating and the associated gravitational wave (GW) background after the inflaton $Z_2$ symmetry is broken during inflation. This symmetry breaking generates both trilinear and quartic inflaton-Higgs interactions during preheating. The quartic inflaton-Higgs coupling is characterized by $q_{\phi h}\equiv \lambda_{\phi h}/\lambda_\phi$, while the trilinear interaction enters jointly through $q_{\phi h}$ and $q_\epsilon\equiv m_\phi/(\sqrt{\lambda_\phi}\phi_0)$. The Higgs self-coupling parameter $q_h\equiv \lambda_h/\lambda_\phi$ determines the onset of backreaction through the effective mass induced by Higgs self-interactions. Our simulations show that efficient preheating requires both a sufficiently broad resonance band and delayed backreaction. For $\lambda_\phi=10^{-13}$, the viable parameter region is approximately $10<q_{\phi h}<10^4$, $q_h<10^3$, and $q_\epsilon<10^{-5}$. Smaller $q_\epsilon$ keeps the system in a quartic-dominated regime and suppresses the rapid drift of resonance bands, while smaller $q_h$ delays the end of preheating by weakening self-interaction-induced backreaction. The amplified Higgs inhomogeneities source GW through the transverse-traceless part of the anisotropic stress tensor. The lattice results show that the GW spectrum grows rapidly during parametric resonance, broadens through rescattering, and saturates in the nonlinear stage. At late times, the spectrum develops a broad peak with amplitude $\Omega_{\rm gw}\sim10^{-6}$ at production. After redshifting to the present day, the peak frequency is $f\sim10^9\,{\rm Hz}$ with present-day amplitude $\Omega_{\rm gw,0} h^2 \sim 10^{-10}$. These results suggest that high-frequency GW from Higgs preheating may be detectable by future resonant-cavity detectors.