Spectrum of high-frequency gravitational waves from graviton bremsstrahlung by the decay of inflaton: case with polynomial potential

We study the generation of high-frequency gravitational waves (GWs) through graviton bremsstrahlung during the decay of inflaton in the post-inflationary universe, focusing on scenarios with a polynomial inflaton potential. Two main reheating channels are considered: decays into bosons (spin 0) and fermions (spin $\frac{1}{2}$). We compute the resulting GW spectra from three-body decays, where the inflaton decays into a pair of daughter particles and a graviton. We numerically compute the GW spectra for various polynomial exponents by employing two distinct approaches: one treating the inflaton as a collection of rest particles and the other treating it as a coherently oscillating classical field. In the former approach, only gravitons with energies below half the inflaton mass are produced, while the latter allows for the production of gravitons with arbitrarily high energies when the potential exponent is 4 or greater. This difference arises because the inflaton's oscillations are no longer described by a single harmonic mode but instead consist of infinitely many harmonic modes with different frequencies. As a result, the GW spectrum exhibits multiple peaks, with these peaks being less pronounced for higher powers of the potential. We also examine the dependence of the GW spectrum on the coupling constant between the inflaton and daughter particles. Our findings suggest that future GW detectors targeting GWs in the GHz band, such as resonant cavities, may have the capability to detect these signals, offering potential insights into the reheating phase of the early universe.