  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.
