Sensitivity of gravitational waves from preheating to a scalar field's interactions

After inflation, a period of preheating may have produced a stochastic background of high frequency gravitational waves (GWs) that would persist until today. The nature of the inflaton's coupling to Standard Model or other fields is unknown, so it is useful to ask what features such fields may typically have, and how these affect predictions for the GW's produced. Here we consider the inflaton to be coupled to a light scalar field, and show that even a very small quartic self-interaction term will reduce the amplitude of the GW spectrum. For self-coupling $\lambda_{\chi} \gtrsim g^2$, where $g^2$ is the inflaton-scalar coupling, the peak energy density goes as $\Omega_{\rm gw}^{(\lambda_{\chi})} / \Omega_{\rm gw}^{(\lambda_{\chi}=0)} \sim (g^2/\lambda_{\chi})^{2}$. A consequence is that if the universe reheats through an inflaton-Higgs coupling then the spectrum would be suppressed but the dynamics would be sensitive to the Higgs potential near the energy scale of inflation.