Irreducible Graviton Floor from Reheating

Inflaton decay inevitably emits gravitons through bremsstrahlung during reheating. We show that the soft part of this emission amplitude, fixed by Weinberg’s soft-graviton theorem, becomes an irreducible stochastic gravitational-wave (GW) background after accounting for cosmological evolution. The theorem fixes the infrared branch of the spectrum, ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}\propto f$, independently of the microscopic operator responsible for inflaton decay, while the normalization is controlled by the hard inflaton decay rate and by a phase-space factor. We carry this out for inflaton $n$-body decays, including the phase-space integrals, finding that the maximum of the spectrum scales as $2\mathrm{/}n$ relative to the $n=2$ case. The signal can reach ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}{h}^2\sim \mathcal{O}({10}^{-17})$ at frequencies above the GHz scale. This predicts a stochastic graviton floor from perturbative reheating: a larger signal would require either other processes beyond perturbative bremsstrahlung or inflationary scenarios beyond conventional single-field slow roll.