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arXiv 2109.08696gr-qchep-th
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带剪切的反弹：量子宇宙学的启示

Bouncing with shear: Implications from quantum cosmology

Karthik Rajeev, Vikramaditya Mondal, Sumanta Chakraborty

备注：
This article is dedicated to the memory of Paddy (Prof. T. Padmanabhan), who incidentally started his monumental career with quantum cosmology
发表信息：
JCAP 01 (2022) 01, 008
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摘要：

我们考虑在一类宇宙学的弹跳模型中引入各向异性。各向异性的存在通常会给弹跳模型带来厄运，因为当宇宙收缩时，由各向异性应力引起的能量密度会超过其他物质成分。在文献中提出了不同的建议，以解决这种病理学，经典。在这里，我们介绍了一个家庭的弹跳模型，其中的剪切密度可以调整到允许或禁止经典的弹跳情况。在此之后，我们表明量子宇宙学的考虑可以彻底改变上述情况。最重要的是，我们发现，量子效应可以使反弹，即使当各向异性应力大到足以禁止相同的经典。我们采用适当的迷你超空间惠勒-德威特方程的均匀，但各向异性的宇宙学的解决方案，与边界条件，宇宙最初收缩。有趣的是，Wheeler-DeWitt方程的解表现出一种有趣的类似相变的行为，其中，在剪切密度达到临界值之前，具有弹跳宇宙的概率精确地为1，然后随着剪切密度的进一步增加，弹跳宇宙的概率开始突然减小。我们使用洛伦兹量子宇宙学的工具以及Picard-Lefschetz理论的应用验证了我们的发现。特别是，反弹的半经典概率已重新推导出的虚部的壳上有效的行动，评估在复杂的鞍点。还讨论了影响和未来的方向。

英文摘要：

We consider the introduction of anisotropy in a class of bouncing models of cosmology. The presence of anisotropy often spells doom on bouncing models, since the energy density due to the anisotropic stress outweighs that of other matter components, as the universe contracts. Different suggestions have been made in the literature to resolve this pathology, classically. Here, we introduce a family of bouncing models, in which the shear density can be tuned to either allow or forbid classical bouncing scenarios. Following this, we show that quantum cosmological considerations can drastically change the above scenario. Most importantly, we find that quantum effects can enable a bounce, even when the anisotropic stress is large enough to forbid the same classically. We employ the solutions of the appropriate mini-superspace Wheeler-DeWitt equation for homogeneous, but anisotropic cosmologies, with the boundary condition that the universe is initially contracting. Intriguingly, the solution to the Wheeler-DeWitt equation exhibit an interesting phase transition-like behaviour, wherein, the probability to have a bouncing universe is precisely unity before the shear density reaches a critical value and then starts to decrease abruptly as the shear density increases further. We verified our findings using the tools of the Lorentzian quantum cosmology, along with the application of the Picard-Lefschetz theory. In particular, the semi-classical probability for a bounce has been re-derived from the imaginary component of the on-shell effective action, evaluated at the complex saddle points. Implications and future directions have also been discussed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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