arXiv 2602.026822026-02-02hep-thastro-ph.COgr-qc

一致评估无边界提议

Consistent Evaluation of the No-Boundary Proposal

Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校莱因韦伯理论物理研究所与物理系）；Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）

Ahmed I. Abdalla, Stefano Antonini, Raphael Bousso, Luca V. Iliesiu, Adam Levine, Arvin Shahbazi-Moghaddam

备注：: 21 pages, 11 pages of appendices, 1 figure

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AI总结：

本文重新审视无边界提议，发现其概率预测为接近或恰好1，并通过膨胀宇宙学示例展示一致评估方法。

摘要：

我们重新审视Hartle-Hawking无边界提议。为了提取概率，必须使用引力路径积分（GPI）来计算不仅无边界幅度，还要用其平方除以的规范。我们发现这会大大改变预测：任何封闭宇宙的概率要么接近1，要么恰好为1。也就是说，在由GPI定义的封闭宇宙希尔伯特空间中，天文学感兴趣的态都几乎与Hartle-Hawking态平行，直到非微扰修正在$G_N^{-1}$中。我们还考虑了GPI的统计解释，作为任意幅值乘积的平均。我们发现在这种情况下，所有幅值都恰好为1，与最近的论点一致，即GPI的统计方法在封闭边界计算时是对一维希尔伯特空间的平均。作为例子，我们展示了在膨胀宇宙学中一致评估无边界提议。

英文摘要：

We revisit the Hartle-Hawking no-boundary proposal. To extract probabilities, one must use the gravitational path integral (GPI) to compute not only the no-boundary amplitude, but also the norms by which its square is divided. We find that this dramatically alters predictions: the probability for any closed universe is either nearly 1, or exactly 1. That is, in the Hilbert space of closed universes defined by the GPI, the states of interest in cosmology are all nearly parallel to the Hartle-Hawking state up to nonperturbative corrections in $G_N^{-1}$. We also consider a statistical interpretation of the GPI, as an average of arbitrary products of amplitudes. We find that all amplitudes are exactly 1 in this case, consistent with recent arguments that the statistical approach to the GPI with a closed boundary computes an average over one-dimensional Hilbert spaces. As an example, we illustrate the consistent evaluation of the no-boundary proposal in inflationary cosmology.

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