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arXiv 1801.07313gr-qcastro-ph.COhep-phhep-th
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从圈量子引力看宇宙动力学

Towards Cosmological Dynamics from Loop Quantum Gravity

Bao-Fei Li, Parampreet Singh, Anzhong Wang

备注：
Version to appear in Phys. Rev. D97, 084029 (2018)
发表信息：
Phys. Rev. D 97, 084029 (2018)
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摘要：

我们提出了一个系统的研究宇宙动力学产生的有效的哈密顿量，最近在圈量子引力使用蒂曼的正则化和早期获得的圈量子宇宙学（LQC）通过保持洛伦兹项明确的哈密顿约束。我们表明，量子几何效应的结果在能量密度的二次修正比LQC造成非奇异反弹。动力学可以用汉密尔顿方程或弗里德曼-雷乔胡里方程来描述，但这两种描述之间的映射不是一对一的。仔细的分析解决了这个模型中对称与不对称反弹的张力，表明反弹必须是不对称的，对称反弹在物理上是不一致的，与标准的LQC相反。此外，目前的观测只允许这样一种情况，即反弹前的分支是渐进的de Sitter，类似于LQC中史瓦西内部的量子化，而反弹后的分支产生经典的广义相对论。对于一个二次势，我们发现一个缓慢的通货膨胀一般发生在反弹之后，这是非常类似的LQC中发生的。

英文摘要：

We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC causing a non-singular bounce. Dynamics can be described by the Hamilton's or the Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one-to-one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the pre-bounce branch is asymptotically de Sitter, similar to a quantization of the Schwarzschild interior in LQC, and the post-bounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.

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