We extend the concept of Hawking-Moss, or up-tunnelling, transitions in the early universe to include black hole seeds. The black hole greatly enhances the decay amplitude, however, order to have physically consistent results, we need to impose a new condition (automatically satisfied for the original Hawking-Moss instanton) that the cosmological horizon area should not increase during tunnelling. We motivate this conjecture physically in two ways. First, we look at the energetics of the process, using the formalism of extended black hole thermodynamics; secondly, we extend the stochastic inflationary formalism to include primordial black holes. Both of these methods give a physical substantiation of our conjecture.

中文翻译：

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霍金-莫斯过渡与黑洞种子

我们将早期宇宙中的霍金-莫斯（Hawking-Moss）或向上隧道转变的概念扩展到包括黑洞种子。黑洞极大地增强了衰减幅度，然而，为了获得物理上一致的结果，我们需要施加一个新条件（自动满足原始霍金-莫斯瞬子），即在隧道挖掘过程中宇宙视界面积不应增加。我们以两种方式在物理上激发了这一猜想。首先，我们使用扩展黑洞热力学的形式来研究该过程的能量学；其次，我们将随机膨胀形式主义扩展到包括原始黑洞。这两种方法都为我们的猜想提供了物理证实。