Relic gravitational waves from cosmological horizon radiation during de Sitter period: as zero-order approximation of inflation

It is well known that the event horizon of the de Sitter universe can produce particles, and one can get sizable Hawking radiation by considering inflationary phases as de Sitter spacetimes with large Hubble rates. In this compact paper, we consider the graviton emission part of these radiations and assume that these graviton signals can exist in the current universe in the form of gravitational waves. We predict an energy density parameter of $\log_{10}(\Omega_{\rm GW} h^2) \sim \mathscr{O}(-25) - \mathscr{O}(-30)$ and its associated peak frequency $\log_{10}(f_{\rm peak}^0) \sim \mathscr{O}(6)-\mathscr{O}(5)$, depending on the reheating temperature. These signals occupy a frequency band below the ultrahigh-frequency regime and possess a detectable energy density, offering a promising target for future gravitational wave observatories. We believe that the detection of such signals would provide a compelling test of Hawking's radiation theory in a cosmological context.