AI 中文总结
本文研究早期宇宙大质量粒子衰变产生的低频引力辐射，通过两种方法计算其能量谱，建立软引力子定理与引力记忆公式的联系，推导宇宙学随机引力能量谱的标度行为，揭示低频信号受抑制的特性。
AI 中文摘要
早期宇宙产生的引力辐射为超出标准模型（SM）的物理提供了有力观测窗口。本文研究大质量粒子衰变产生的引力辐射的低频尾，闵可夫斯基时空中的能量谱dE/dω呈现两个不同区域：特征截断频率以上为平坦的轫致辐射/记忆谱，以下为受抑制的二次频率标度；截断频率由衰变产物的典型动量变化率决定。我们通过两种独立且等价的方法计算dE/dω：利用Weinberg软引力子定理和求解运动方程，这进一步建立了Weinberg软引力子定理与引力记忆公式的联系，我们将该公式推广以包含末态散射效应。随后计算早期宇宙中大量粒子衰变产生的宇宙学随机引力能量谱h²Ω_h，证明h²Ω_h在截断频率以上呈线性标度，以下转变为三次标度；我们的发现显示，与简单线性外推相比，低频信号受到抑制，这对探测前景有影响，同时揭示了早期宇宙宇宙学随机引力能量谱背景下轫致辐射与记忆效应的关联。
英文摘要
Gravitational radiation from the early Universe offers a powerful window into physics beyond the Standard Model (SM). In this paper, we investigate the low-frequency tail of gravitational radiation produced by the decay of massive particles. The energy spectrum in Minkowski space-time, $dE/dω$, exhibits two distinct regimes: a flat bremsstrahlung/memory spectrum above a characteristic cutoff frequency and a suppressed quadratic frequency scaling below it. The typical rate of momentum change of the decay products determines the cutoff frequency. We calculate $dE/dω$ in two independent but equivalent ways: using Weinberg's soft graviton theorem and by solving the equations of motion. This further establishes the connection between Weinberg's soft graviton theorem and the gravitational memory formula, which we generalize to incorporate the effects of final-state scattering. We then compute the cosmological stochastic gravitational energy spectrum $h^2Ω_{\rm h}$ generated by many particle decays in the early Universe. We demonstrate that $h^2Ω_{\rm h}$ exhibits linear scaling with frequency above the cutoff frequency, transitioning to cubic scaling below it. Our findings reveal a suppression of the low-frequency signal compared to a naive linear extrapolation, with implications for detection prospects. Our results also reveal the connection between bremsstrahlung and memory in the context of cosmological stochastic gravitational energy spectra from the early Universe.
