平滑与瞬时暴胀转变：重新审视最陡增长与原初黑洞
Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes
AI总结：
本文在单时钟暴胀框架下研究背景参数转变速度对原初黑洞形成的影响，证明平滑转变可消除瞬时转变伪影，并揭示PBH质量分布主要取决于功率谱峰值振幅和平台期而非增长陡度。
摘要：
原初黑洞（PBHs）可以通过早期宇宙中的多种机制产生。一个将PBHs与暴胀现象学联系起来的特定形成渠道，需要在小尺度上增强的原初曲率扰动。在本文中，我们在单时钟暴胀的背景下，考察背景能够在哈勃层级参数的不同取值之间转变的速度有多快，而这一转变最终必须源自对背景暴胀场的一致导数展开。我们讨论了与瞬时或极快速转变相关的伪影，并考虑了其对最陡功率谱增长和PBH形成的影响。特别地，我们强调了先前在具有保守平滑转变的单场暴胀中发现的$k^4$最陡增长的稳健性，以及功率谱振幅能够增长多少的限制，并证明PBH质量分布对这些伪影敏感，当转变被平滑时这些伪影会消失。我们还表明，质量分布对功率谱增长及随后衰减的陡峭程度相对不敏感，主要取决于峰值振幅以及是否存在持续超过一个e-fold的平台期。当然，功率谱的形状可以通过其他示踪物加以约束，因此理解其形状的物理限制仍然是一个相关的问题。
英文摘要：
Primordial black holes (PBHs) can be produced by a range of mechanisms in the early universe. A particular formation channel that connects PBHs with inflationary phenomenology invokes enhanced primordial curvature perturbations at small scales. In this paper, we examine how rapidly the background can transition between different values of the parameters of the Hubble hierarchy in the context of single-clock inflation, which must ultimately derive from a consistent derivative expansion for the background inflaton field. We discuss artefacts associated with instant or very rapid transitions, and consider the impact on the steepest power spectrum growth and the formation of PBHs. In particular, we highlight the robustness of the $k^4$ steepest growth previously found for single-field inflation with conservatively smoothed transitions and limits on how much the amplitude of the power spectrum can grow, and demonstrate that the PBH mass distribution is sensitive to the artefacts, which go away when the transitions are smoothed. We also show that the mass distribution is relatively insensitive to the steepness of the growth and subsequent decay of the power spectrum, depending primarily on the peak amplitude and the presence of any plateaus that last more than an e-fold. The shape of the power spectrum can of course be constrained by other tracers, and so understanding the physical limitations on its shape remains a pertinent question.
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