标题： 原初黑洞在 inflation 期间的量子扩散聚类 显示英文标题

标题： Clustering of primordial black holes from quantum diffusion during inflation

摘要： 我们研究了在暴胀期间存在量子扩散的情况下，大涨落如何在空间上相关联。 这是通过在随机的$\delta N$形式主义中计算实空间关联函数来实现的。 我们首先推导出由暴胀结束时的局域观测者所测量到的实际距离的精确描述，改进了先前的工作。 我们的方法基于递归算法技术，这些技术一致地包括体积加权效应。 然后我们提出了一种“大体积”近似法，在这种近似下，计算可以仅使用首通时间分析完成，并由此推导出一个新的关于随机暴胀功率谱的公式。 接着我们研究了曲率扰动的完整两点统计量。 由于存在指数尾部，我们发现大涨落的联合分布形式为$P(\zeta_{R_1}, \zeta_{R_2}) = F(R_1,R_2,r) P(\zeta_{R_1})P( \zeta_{R_2})$，其中$\zeta_{R_1}$和$\zeta_{R_2}$表示在两个相距$r$的空间点处以半径$R_1$和$R_2$粗粒化后的曲率扰动。 这意味着，在尾部，定义为$P(\zeta_{R_1}>\zeta_{\rm{c}}, \zeta_{R_2}>\zeta_{\rm{c}})/[P(\zeta_{R_1}>\zeta_{\rm{c}}) P(\zeta_{R_2}>\zeta_{\rm{c}})]-1$的归一化关联函数与阈值$\zeta_{\rm{c}}$无关。 这与高斯统计形成对比，在高斯统计中，同一量会随着$\zeta_{\rm{c}}$强烈衰减，并表明所有在指数尾部形成的结构都具有普适的聚类分布特征。 在中间（即尚未达到指数形式）的尾部形成的结构可能表现出不同的、依赖于模型的行为。 显示英文摘要

摘要： We study how large fluctuations are spatially correlated in the presence of quantum diffusion during inflation. This is done by computing real-space correlation functions in the stochastic-$\delta N$ formalism. We first derive an exact description of physical distances as measured by a local observer at the end of inflation, improving on previous works. Our approach is based on recursive algorithmic methods that consistently include volume-weighting effects. We then propose a "large-volume'' approximation under which calculations can be done using first-passage time analysis only, and from which a new formula for the power spectrum in stochastic inflation is derived. We then study the full two-point statistics of the curvature perturbation. Due to the presence of exponential tails, we find that the joint distribution of large fluctuations is of the form $P(\zeta_{R_1}, \zeta_{R_2}) = F(R_1,R_2,r) P(\zeta_{R_1})P( \zeta_{R_2})$, where $\zeta_{R_1}$ and $\zeta_{R_2}$ denote the curvature perturbation coarse-grained at radii $R_1$ and $R_2$, around two spatial points distant by $r$. This implies that, on the tail, the reduced correlation function, defined as $P(\zeta_{R_1}>\zeta_{\rm{c}}, \zeta_{R_2}>\zeta_{\rm{c}})/[P(\zeta_{R_1}>\zeta_{\rm{c}}) P(\zeta_{R_2}>\zeta_{\rm{c}})]-1$, is independent of the threshold value $\zeta_{\rm{c}}$. This contrasts with Gaussian statistics where the same quantity strongly decays with $\zeta_{\rm{c}}$, and shows the existence of a universal clustering profile for all structures forming in the exponential tails. Structures forming in the intermediate (i.e. not yet exponential) tails may feature different, model-dependent behaviours.