AI 中文总结
研究原始曲率谱局部增强产生的共形费米子暗物质和引力波背景，通过暗物质丰度确定标量归一化，将兆赫兹信号与暗物质相关量联系，单场实现展示机制，建立小尺度暴胀等与实验室搜索的可检验联系。
AI 中文摘要
原始曲率谱的局部增强会留下两种不同的遗迹：引力产生的共形费米子暗物质和标量诱导的随机引力波背景。我们表明，暗物质丰度通过曲率谱的三次矩确定标量归一化，而诱导的张量信号探测其二阶卷积。这消除了标量诱导引力波模板中通常的归一化自由度，并将兆赫兹信号直接与暗物质质量、峰值尺度和谱宽度联系起来。一个具体的单场实现展示了这种机制：穆哈诺夫 - 佐佐木演化产生一个宽阔的兆赫兹背景，其安全地低于高斯原始黑洞阈值。在此结构中，零高频搜索成为共形费米子质量的下限，而一次探测必须从一个原始特征重现遗迹丰度、峰值频率、幅度和宽度。结果是在小尺度暴胀结构、超重暗物质和实验室兆赫兹引力波搜索之间建立了一个可检验的联系。
英文摘要
A localized enhancement of the primordial curvature spectrum can leave two distinct relics: gravitationally produced conformal-fermion dark matter and a scalar-induced stochastic gravitational-wave background. We show that the dark-matter abundance fixes the scalar normalization through the cubic moment of the curvature spectrum, while the induced tensor signal probes its quadratic convolution. This closes the usual normalization freedom in scalar-induced gravitational-wave templates and ties the MHz signal directly to the dark-matter mass, peak scale, and spectral width. A concrete single-field realization demonstrates this mechanism: a Mukhanov--Sasaki evolution produces a broad MHz background that sits safely below the Gaussian primordial-black-hole threshold. In this construction, a null high-frequency search becomes a lower bound on the conformal-fermion mass, while a detection has to reproduce the relic abundance, peak frequency, amplitude, and width from one primordial feature. The result is a testable link between small-scale inflationary structure, superheavy dark matter, and laboratory MHz gravitational-wave searches
Comments14 pages, 8 figures
