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arXiv 0910.1876astro-ph.CO
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非线性微扰理论中的原初黑洞

Primordial Black Holes in non-linear perturbation theory

Juan Carlos Hidalgo

摘要:

本论文从研究宇宙学涨落的起源开始,特别关注非高斯关联函数很大的情况。分析表明,来自几乎无质量的辅助场的扰动一般产生大的非线性参数fNL值。通过构造一个非高斯概率分布函数(PDF),探讨了在宇宙结构统计中引入非高斯关联函数的影响。这样的PDF是从量子场论的背景下,与n点关联函数作为唯一的输入的第一性原理推导出的共动曲率微扰。然后,非高斯PDF被用来探讨两个重要的问题,在物理学的原始黑洞(PBH):第一,计算非高斯修正产生的原始曲率起伏的PBH的数量。第二个应用是关于新的宇宙学观测量。已知PBH的形成取决于两个主要的物理特征:由初始曲率不均匀性产生的引力场的强度和曲率位形边缘的压力梯度。我们占找到这些配置的概率,通过使用两个参数:振幅的不均匀性和它的二阶径向导数,在配置的中心进行评估。导出的概率在宇宙中的PBH的形式的质量分数的影响进行了讨论。

英文摘要:

This thesis begins with a study of the origin of cosmological fluctuations with special attention to those cases in which the non-Gaussian correlation functions are large. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameter f_NL. The effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored by constructing a non-Gaussian probability distribution function (PDF). Such PDF is derived for the comoving curvature perturbation from first principles in the context of quantum field theory, with n-point correlation functions as the only input. The non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs): First, to compute non-Gaussian corrections to the number of PBHs generated from the primordial curvature fluctuations. The second application concerns new cosmological observables. The formation of PBHs is known to depend on two main physical characteristics: the strength of the gravitational field produced by the initial curvature inhomogeneity and the pressure gradient at the edge of the curvature configuration. We account for the probability of finding these configurations by using two parameters: The amplitude of the inhomogeneity and its second radial derivative, evaluated at the centre of the configuration. The implications of the derived probability for the fraction of mass in the universe in the form of PBHs are discussed.

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