Dependence of the amplitude of gravitational waves from preheating on the inflationary energy scale

Abstract

Stochastic gravitational wave backgrounds receive increasing attention and provide a new possibility to directly probe the early Universe. In the preheating process at the end of inflation, parametric resonance can generate large energy density perturbations and efficiently produce gravitational waves (GWs) which carry unique information about inflation. Since the peak frequency of such GWs is approximately proportional to the inflationary energy scale, ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$, GWs from preheating are expected to be observed by interferometer GW detectors in low-scale inflationary models. We investigate a class of preheating models where the effective potential has a quadratic minimum, and the dependence of the amplitude of such GWs on ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$, then find that the present energy spectrum of these GWs does not depend on ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ except in the case where ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ is above a critical value ${\mathrm{\ensuremath{\Lambda}}}_{c}$---a parameter depending on the resonance strength. We numerically obtain ${\mathrm{\ensuremath{\Lambda}}}_{c}$ in terms of the model parameters in a linear approximation and then conduct lattice simulations to verify this result. For ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}\ensuremath{\lesssim}{\mathrm{\ensuremath{\Lambda}}}_{c}$, the amplitude of GWs quickly decreases with ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ and becomes challenging to observe. In turn, observing such GWs in interferometer detectors also helps to determine ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{inf}}$ and the resonance strength during the preheating.