原初黑洞（PBH）可以从暴涨后大的原初涨落中产生，在这个过程中也会 伴随着诱导引力波（GW）的产生。本文即针对早期宇宙中暴涨之后和大爆炸 核合成（BBN）之前的这段时期产生的 PBHs 和 GWs 的形成机制和演化以及 之间的联系进行了讨论。针对 PBHs，本文从宇宙学基本知识出发推导其演化 微分方程并且给出 PBH 演化过程图示，显示出 PBH 形成时其密度分数 和 质量 MPBH,f 的重要性，并且在最后分析了两者对宇宙占主导地位成分的影 响。针对诱导 GWs，本文从宇宙学微扰理论出发，首先推导其宇宙背景下对 应的物理关系，其次利用一阶标量微扰得到原初涨落时对应的微扰量，它们作 为诱导引力波的源进入张量微扰里。通过计算可以发现有效的源项与 ^-3成 正比，引力波的谱密度与 2 成正比，与 MPBH,f ^-3/2 成正比。

Primordial black holes (PBH) can emerge from large primordial fluctuations following inflation, which are also accompanied by the generation of induced gravitational waves (GW). In this paper, we discuss the formation mechanism and evolution of PBHs and GWs in the early universe after inflation and before Big Bang Nucleosynthesis (BBN). For PBHs, this paper deduces its evolution differential equation from the basic knowledge of cosmology and gives the diagram of the evolution process of PBH, showing the importance of the density fraction and the mass M_PBH,f during the formation of PBH, and finally analyzes the influence of both on the dominant components of the universe. For induced GWs, based on cosmological perturbation theory, this paper first deduces the corresponding physical relationship in the cosmic background, and then uses first-order scalar perturbations to obtain the corresponding perturbations in the original fluctuation, which are used as the source of induced gravitational waves into the tensor perturbations. Through calculation, it can be found that the effective source term is proportional to ^-3, and the spectral density of the gravitational wave is proportional to ² , and is proportional to M_, ^-3/2 .