Title: Gravitational wave production from preheating: parameter dependence,
Abstract: Parametric resonance is among the most efficient phenomena generating
gravitational waves (GWs) in the early Universe. The dynamics of parametric
resonance, and hence of the GWs, depend exclusively on the resonance parameter
$q$. The latter is determined by the properties of each scenario: the initial
amplitude and potential curvature of the oscillating field, and its coupling to
other species. Previous works have only studied the GW production for fixed
value(s) of $q$. We present an analytical derivation of the GW amplitude
dependence on $q$, valid for any scenario, which we confront against numerical
results. By running lattice simulations in an expanding grid, we study for a
wide range of $q$ values, the production of GWs in post-inflationary preheating
scenarios driven by parametric resonance. We present simple fits for the final
amplitude and position of the local maxima in the GW spectrum. Our
parametrization allows to predict the location and amplitude of the GW
background today, for an arbitrary $q$. The GW signal can be rather large, as
$h^2\Omega_{\rm GW}(f_p) \lesssim 10^{-11}$, but it is always peaked at high
frequencies $f_p \gtrsim 10^{7}$ Hz. We also discuss the case of
spectator-field scenarios, where the oscillatory field can be e.g.~a curvaton,
or the Standard Model Higgs.