arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1906.09007hep-thastro-ph.COgr-qc
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暴胀的量子不完全性

Quantum Incompleteness of Inflation

Alice Di Tucci, Job Feldbrugge, Jean-Luc Lehners, Neil Turok

摘要:

暴胀最常使用量子场论(QFT)在固定的弯曲时空背景下描述。这样的描述是有效的,只有当所考虑的区域的空间体积是如此之大,其大小和形状模量表现经典。然而,如果我们将膨胀的宇宙追溯到早期,任何感兴趣的共同运动区域的体积-例如现在的哈勃体积-都会变得指数级小。因此,背景轨道中的量子涨落在早期是不能忽略的。在本文中,我们开发了一个平坦的,膨胀补丁(近似为德西特时空)的路径积分描述,处理的背景标度因子和引力波扰动量子力学。我们发现这种描述失败的初始比例因子的小值,因为\emph{two}背景鞍点解决方案有助于路径积分。这导致了弯曲时空中QFT的崩溃,导致波动不稳定和失控。我们表明,这个问题可能会得到缓解的量子初始条件的仔细选择,为背景和波动,提供的初始,膨胀补丁的体积大于$\gg H^{-1}$在普朗克单位与$H$的哈勃常数在开始膨胀。补救的代价是高昂的:不仅通货膨胀的背景,而且稳定的Bunch-Davies波动也必须手工输入。我们的讨论强调,即使暴胀尺度远低于普朗克质量,也需要新的物理学来解释宇宙的初始量子态。

英文摘要:

Inflation is most often described using quantum field theory (QFT) on a fixed, curved spacetime background. Such a description is valid only if the spatial volume of the region considered is so large that its size and shape moduli behave classically. However, if we trace an inflating universe back to early times, the volume of any comoving region of interest -- for example the present Hubble volume -- becomes exponentially small. Hence, quantum fluctuations in the trajectory of the background cannot be neglected at early times. In this paper, we develop a path integral description of a flat, inflating patch (approximated as de Sitter spacetime), treating both the background scale factor and the gravitational wave perturbations quantum mechanically. We find this description fails at small values of the initial scale factor, because \emph{two} background saddle point solutions contribute to the path integral. This leads to a breakdown of QFT in curved spacetime, causing the fluctuations to be unstable and out of control. We show the problem may be alleviated by a careful choice of quantum initial conditions, for the background and the fluctuations, provided that the volume of the initial, inflating patch is larger than $\gg H^{-1}$ in Planck units with $H$ the Hubble constant at the start of inflation. The price of the remedy is high: not only the inflating background, but also the stable, Bunch-Davies fluctuations must be input by hand. Our discussion emphasizes that, even if the inflationary scale is far below the Planck mass, new physics is required to explain the initial quantum state of the universe.

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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