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arXiv 1702.02552gr-qcastro-ph.COhep-th
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具有自由初始条件的引力：可由CMB B模偏振检验的宇宙学常数问题的解

Gravity with free initial conditions: a solution to the cosmological constant problem testable by CMB B-mode polarization

Tomonori Totani

备注：
10 pages, no figure. Accepted by Phys. Rev. D
发表信息：
Phys. Rev. D 96, 084062 (2017)
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摘要：

在标准的广义相对论中，宇宙不能以任意的初始条件开始，因为爱因斯坦场方程（EFE）的十个分量中有四个是对初始条件的约束。在以前的工作中，有人建议扩展引力理论，允许自由的初始条件，与动机解决宇宙学常数的问题。这是通过对作用量原理中的度量变化设置四个约束来实现的，这是合理的，因为重力的物理自由度最多为六。然而，这个理论有两个问题：除了幺模条件之外的三个约束没有明确的物理意义，平坦闵可夫斯基时空对扰动是不稳定的。这里，一组新的引力场方程的推导，取代了新的约束条件，要求测地线路径保持测地线对度量变化。不稳定的问题自然就解决了。对宇宙学常数$Λ$的影响是不变的;通过暴胀，理论收敛到$Λ$不为零的EFE，但是$Λ$在比现在的哈勃视界大得多的尺度上变化。然后星系只在小的$Λ$区域形成，人择论证解决了宇宙学常数问题。由于度规动力学中自由度的增加，该理论预言了在暴胀期间量子涨落产生的新的非振荡度规各向异性模式，并且CMB B模式偏振将与广义相对论的标准预测不同。

英文摘要：

In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was proposed to extend the gravity theory to allow free initial conditions, with a motivation to solve the cosmological constant problem. This was done by setting four constraints on metric variations in the action principle, which is reasonable because the gravity's physical degrees of freedom are at most six. However, there are two problems about this theory; the three constraints in addition to the unimodular condition were introduced without clear physical meanings, and the flat Minkowski spacetime is unstable against perturbations. Here a new set of gravitational field equations is derived by replacing the three constraints with new ones requiring that geodesic paths remain geodesic against metric variations. The instability problem is then naturally solved. Implications for the cosmological constant $Λ$ are unchanged; the theory converges into EFE with nonzero $Λ$ by inflation, but $Λ$ varies on scales much larger than the present Hubble horizon. Then galaxies are formed only in small $Λ$ regions, and the cosmological constant problem is solved by the anthropic argument. Because of the increased degrees of freedom in metric dynamics, the theory predicts new non-oscillatory modes of metric anisotropy generated by quantum fluctuation during inflation, and CMB B-mode polarization would be observed differently from the standard predictions by general relativity.

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