Statistics of coarse-grained cosmological fields in stochastic inflation
Statistics of coarse-grained cosmological fields in stochastic inflation
复制标题
随机暴涨中粗粒度宇宙场的统计
DOI：
10.1088/1475-7516/2022/02/021
复制
发表时间：
2022
影响因子：
6.4
通讯作者：
Vennin Vincent
中科院分区：
文献类型：
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作者：
Tada Yuichiro;Vennin Vincent
我们提出了一个通用框架来计算宇宙扰动的单点统计量，在任意尺度 R 上进行粗粒度处理，并且存在量子扩散。利用随机 δ N 形式，我们展示了它如何与尺度 R 超出哈勃半径之前实现的膨胀量的统计相关。这使我们得到了曲率扰动的概率密度函数（PDF）、同动密度对比和压缩函数的明确公式。然后，我们将我们的形式主义应用于计算在包含“量子阱”（即势中完全平坦的区域）的单场模型中产生的原初黑洞的质量分布。我们确认 PDF 具有重的指数尾部，并且在曲率扰动的情况下具有额外的三次抑制。研究表明，质量分布的大质量端主要是由随机污染效应驱动的，这种效应产生的黑洞质量比天真的预期的要大。这项工作弥合了随机暴胀形式主义与原始黑洞等天体物理物体质量分布计算之间的最终差距，并开辟了我们最终讨论的各种前景。
We present a generic framework to compute the one-point statistics of cosmological perturbations, when coarse-grained at an arbitrary scale R, in the presence of quantum diffusion. Making use of the stochastic-δ N formalism, we show how it can be related to the statistics of the amount of expansion realised until the scale R crosses out the Hubble radius. This leads us to explicit formulae for the probability density function (PDF) of the curvature perturbation, the comoving density contrast, and the compaction function. We then apply our formalism to the calculation of the mass distribution of primordial black holes produced in a single-field model containing a" quantum well"(ie an exactly flat region in the potential). We confirm that the PDFs feature heavy, exponential tails, with an additional cubic suppression in the case of the curvature perturbation. The large-mass end of the mass distribution is shown to be mostly driven by stochastic-contamination effects, which produce black holes more massive than those naively expected. This work bridges the final gap between the stochastic-inflation formalism and the calculation of the mass distribution of astrophysical objects such as primordial black holes, and opens up various prospects that we finally discuss.