Primordial black hole formation in the early universe: critical behaviour and self-similarity
Ilia Musco, John C. Miller
备注：
23 pages, 8 figures, new abstract, submitted to Classical and Quantum Gravity. This new version of the paper has been completely rewritten with respect the previous one, with several changes and substantial additional work
Following on after three previous papers discussing the formation of primordial black holes during the radiative era of the early universe, we present here a further investigation of the critical nature of the process involved, aimed at making contact with some of the basic underlying ideas from the literature on critical collapse. We focus on the intermediate state, which we have found appearing in cases with perturbations close to the critical limit, and examine the connection between this and the similarity solutions which play a fundamental role in the standard picture of critical collapse. We have derived a set of self-similar equations for the null-slicing form of the metric which we are using for our numerical calculations, and have then compared the results obtained by integrating these with the ones coming from our simulations for collapse of cosmological perturbations within an expanding universe. We find that the similarity solution is asymptotically approached in a region which grows to cover both the contracting matter and part of the semi-void which forms outside it. Our main interest is in the situation relevant for primordial black hole formation in the radiative era of the early universe, where the relation between the pressure $p$ and the energy density $e$ can be reasonably approximated by an expression of the form $p = we$ with $w=1/3$. However, we have also looked at other values of $w$, both because these have been considered in previous literature and also because they can be helpful for giving further insight into situations relevant for primordial black hole formation. As in our previous work, we have started our simulations with initial supra-horizon scale perturbations of a type which could have come from inflation.
Primordial black hole induced gravitational waves in $f(R)$ gravity
University of Patras（帕特雷大学）；Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Università di Napoli “Federico II”（那不勒斯费德里科二世大学）
Power spectrum of density fluctuations, halo abundances and clustering with primordial black holes
我们研究了暗物质（DM）被封装在原始黑洞（PBH）的密度波动$P(k)$的功率谱的影响，我们也看看它对晕的丰度和他们的集群的影响。我们允许泊松波动的增长，因为物质和辐射平等和研究单色和扩展PBH质量分布。我们提出了更新的单色黑洞的质量约束，要求$<10\%$的$Λ$冷暗物质功率谱的$k=1$ hMpc $^{-1}$的规模偏差。我们的结果表明，质量为$>10^4$ h $^{-1}M_\odot$的PBH被排除在宇宙中所有DM的符合之外。我们还将此条件应用于扩展的Press-Schechter（PS）质量函数，并发现即使在应用进化之前，泊松幂也与尺度相关。我们发现特征质量$M^*\leq10^2 $ h $^{-1}M_\odot$是允许的，{当与先前的约束结合时，仅留下PS质量函数的两个特征PBH质量窗口，在$M^*\sim10^2$ h $^{-1}M_\odot$和$\sim10^{-8}$ h $^{-1}M_\odot$，其中所有DM可以在PBH中。在这些窗口内产生的DM晕质量函数与由基本粒子组成的冷暗物质产生的质量函数相似。然而，一旦参数产生不切实际的$P(k)$，所产生的晕质量函数及其偏差作为晕质量的函数，强烈偏离在真实宇宙中测量的行为。
