arXiv 1207.46572012-07-19gr-qcastro-ph.COhep-th

圈量子宇宙学中的签名变化

Signature change in loop quantum cosmology

Jakub Mielczarek

备注：: Proceeding of the conference "Relativity and Gravitation - 100 Years after Einstein in Prague", Prague, June 2012

摘要：

威克旋转通常只被认为是一种有用的计算技巧。然而，正如哈特尔和霍金在80年代初提出的那样，威克旋转可能在普朗克时代获得物理意义。虽然这种可能性在概念上是有趣的，导致无边界的建议，背后的签名变化的机制仍然是神秘的。我们表明，哈特尔和霍金预期的签名变化自然出现在圈量子宇宙学。讨论了具有量子完整效应的宇宙学扰动理论。这是由Cailleteau \textit{et al.}（Class.定量重力{ \bf 29}（2012）095010），该理论可以以无异常的方式唯一地公式化。得到的代数的有效约束原来是修改，使度量签名是从洛伦兹在低曲率政权的高曲率政权的欧几里德。讨论了这一现象对宇宙学扰动传播的影响，并导出了标量和张量扰动的暴胀功率谱的修正。与其他方法的量子引力的可能关系进行了概述。我们还提出了一个直观的解释所观察到的签名的变化，使用类比的自发对称性破缺在“有线”的超材料。

英文摘要：

The Wick rotation is commonly considered only as an useful computational trick. However, as it was suggested by Hartle and Hawking already in early eighties, Wick rotation may gain physical meaning at the Planck epoch. While such possibility is conceptually interesting, leading to no-boundary proposal, mechanism behind the signature change remains mysterious. We show that the signature change anticipated by Hartle and Hawking naturally appear in loop quantum cosmology. Theory of cosmological perturbations with the effects of quantum holonomies is discussed. It was shown by Cailleteau \textit{et al.} (Class. Quant. Grav. {\bf 29} (2012) 095010) that this theory can be uniquely formulated in the anomaly-free manner. The obtained algebra of effective constraints turns out to be modified such that the metric signature is changing from Lorentzian in low curvature regime to Euclidean in high curvature regime. Implications of this phenomenon on propagation of cosmological perturbations are discussed and corrections to inflationary power spectra of scalar and tensor perturbations are derived. Possible relations with other approaches to quantum gravity are outlined. We also propose an intuitive explanation of the observed signature change using analogy with spontaneous symmetry breaking in "wired" metamaterials.

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