In this article, we investigate the stochastic gravitational waves (GWs) spectrum, resulting from the emission of gravitons through bremsstrahlung, in the decay of particles produced by Hawking radiation. Although particle decays inevitably entail the emission of graviton due to bremsstrahlung, the associated decay width is notably suppressed due to the Planck scale suppression in the coupling of matter fields to gravitons. Consequently, the relic abundance of such GWs constituted of these gravitons undergoes a corresponding reduction. However, we demonstrate that super-heavy particles, reaching masses as high as Planck scale, can emerge naturally in the Hawking radiation of evaporating primordial black holes (PBHs) and can compensate for this suppression. In addition, we also discuss the stochastic gravitational waves constituted out of the gravitons directly radiated from such evaporating PBHs. When the super-heavy particle decays promptly after its production, then the corresponding GW spectrum remains subdominant to the one arising from direct PBH evaporation. However, if this particle is long-lived and decays after PBH evaporation, then the resulting GWs produced in these two processes have two distinct spectra with their peaks at extremely high frequencies, providing avenues for proposed ultra-high frequency gravitational wave detectors. We also show that such gravitational waves contribute significantly to substantial dark radiation, which can be probed with the enhanced sensitivity of future experiments.

中文翻译：

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引力波源于原始黑洞蒸发的大质量粒子的衰变


在本文中，我们研究了霍金辐射产生的粒子衰变过程中通过轫致辐射发射引力子而产生的随机引力波 (GW) 谱。尽管粒子衰变不可避免地会由于轫致辐射而导致引力子的发射，但由于物质场与引力子耦合中的普朗克尺度抑制，相关的衰变宽度明显受到抑制。因此，由这些引力子构成的引力波的遗迹丰度相应减少。然而，我们证明，质量达到普朗克尺度的超重粒子可以在蒸发的原初黑洞（PBH）的霍金辐射中自然出现，并且可以补偿这种抑制。此外，我们还讨论了由这种蒸发的PBH直接辐射的引力子构成的随机引力波。当超重粒子在产生后迅速衰变时，相应的引力波谱仍然次于直接PBH蒸发产生的引力波谱。然而，如果这种粒子寿命较长，并且在 PBH 蒸发后衰变，那么这两个过程中产生的引力波将具有两个不同的光谱，其峰值位于极高频率，为提出的超高频引力波探测器提供了途径。我们还表明，这种引力波对大量暗辐射有显着贡献，可以通过未来实验增强的灵敏度来探测暗辐射。