Gravitational Wave Spectrum from the Production of Dark Matter via the freeze-in Mechanism

Since the first detection of gravitational waves by ground-based interferometers, it has emerged as a novel probe for exploring physics in the early universe. The particle nature of cold dark matter (DM) and its underlying production mechanisms remain long-standing unresolved issues in the field. Notably, if DM is generated through the freeze-in mechanism in the early universe, direct laboratory detection becomes extraordinarily challenging due to its extremely weak coupling with standard model particles. In this study, we calculate the graviton bremsstrahlung process involved in the freeze-in production of dark matter, deriving the gravitational wave spectra for both the conventional freeze-in mechanism and ultraviolet freeze-in scenarios. Our analysis reveals that these spectra exhibit distinct characteristics, though they fall beyond the detection limits of currently proposed gravitational wave experiments. However, advancements in high-frequency gravitational wave detection technologies in the future may offer a means to indirectly probe the ultraviolet freeze-in mechanism.