Minimal Production of Prompt Gravitational Waves during Reheating

Abstract: The inflationary reheating phase begins when accelerated expansion ends. As all Standard Model particles are coupled to gravity, gravitational interactions will lead to particle production. This includes the thermal bath, dark matter and gravitational radiation. Here, we compute the spectrum of gravitational waves from the inflatoncondensate during the initial phase of reheating. As particular examples of inflation, we consider the Starobinsky model and T-models, all of which are in good phenomenological agreement with CMB anisotropy measurements. The T-models are distinguished by the shape of the potential about its minimum and can be approximated by $V \sim \phi^k$, where $\phi$ is the inflaton. Interestingly, the shape of the gravitational wave spectrum (when observed) can be used to distinguish among the models considered. As we show, the Starobinsky model and T-models with $k=2$, provide very different spectra when compared to models with $k=4$ or $k>4$. Observation of multiple harmonics in the spectrum can be interpreted as a direct measurement of the inflaton mass. Furthermore, the cutoff in frequency can be used to determine the reheating temperature.