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arXiv 1309.3045gr-qchep-th
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Brans-Dicke引力的Jordan框架与Einstein框架的比较

A comparison between Jordan and Einstein frames of Brans-Dicke gravity a la loop quantum cosmology

Michal Artymowski, Yonnge Ma, Xiangdong Zhang

摘要:

众所周知,在经典的Brans-Dicke理论中,如果物理时空采用同一个度规,那么Jordan框架和Einstein框架是等价的。然而,本文通过宇宙学模型表明,在两个不同的框架中的圈量子化将导致不等价的有效理论。在两种坐标系下,我们分别在真空和附加无质量标量场两种情况下得到了无势有效圈量子Brans-Dicke宇宙学的解析解.在Einstein坐标系下,得到了Brans-Dicke势$\proptoφ^2$的解析解,在这些解中,标度因子在Planck区域附近的跳跃演化。两个帧的循环量化之间的差异通过以下来反映:(i)反弹周围的比例因子的演变,(ii)物理乔丹帧中的反弹的比例。

英文摘要:

It is well known that the Jordan and Einstein frames are equivalent to each other in classical Brans-Dicke theory, provided that one and the same metric is employed for the physical space-time. Nevertheless, it is shown in this paper by cosmological models that the loop quantisation in the two different frames will lead to inequivalent effective theories. Analytical solutions have been found in both frames for the effective loop quantum Brans-Dicke cosmology without potential in: (i) vacuum case, (ii) additional massless scalar field case. In Einstein frame the analytical solution for the Brans-Dicke potential $\proptoφ^2$ has been found. In all of those solutions the bouncing evolution of the scale factor has been obtained around Planck regime. The differences between the loop quantisation of the two frames are reflected by: (i) the evolution of the scale factor around the bounce, (ii) the scale of the bounce in the physical Jordan frame.

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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