标题： 早期物质主导时期产生的引力波的临界行为和紫外尺度特性 显示英文标题

标题： Critical behavior and ultraviolet scaling of induced gravitational waves from an early matter-dominated era

摘要： 诱导引力波(GWs)在早期物质主导(eMD)时期的临界行为和紫外尺度，在原初黑洞蒸发的背景下进行了研究。eMD的深度由宇宙在此阶段可以达到的状态方程最小参数$\omega_{\min}$来表征。我们确定了一个临界值$\omega_{c}\sim 7.3\times10^{-3}$，它区分了两种不同的模式。对于$\omega_{\min}<\omega_{c}$，引力波峰值位于非线性截止点，需要非线性动力学。对于$\omega_{\min}>\omega_{c}$，峰值来源于在物质-辐射相等附近重新进入的模式，其紫外尾部遵循一种不同的尺度$k^{-3/2}$。这种临界行为为深eMD与浅eMD提供了明确的定义，并为未来的引力波观测提供了稳健的光谱特征。 显示英文摘要

摘要： Critical behavior and ultraviolet scaling of induced gravitational waves (GWs) from an early matter-dominated (eMD) era are studied in the context of primordial black hole evaporation. The depth of the eMD is characterized by the minimum parameter of the equation of state $\omega_{\min}$ that the Universe can attain during this phase. We identify a critical value $\omega_{c}\sim 7.3\times10^{-3}$ that separates two regimes. For $\omega_{\min}<\omega_{c}$, the GW peak lies at the non-linear cut-off point and requires non-linear dynamics. For $\omega_{\min}>\omega_{c}$, the peak originates from modes that reenter near the matter-radiation equality, and the ultraviolet tail follows a distinct scaling $k^{-3/2}$. This critical behavior provides a clear definition of deep versus shallow eMD and a robust spectral signature for future GW observations.