论文标题
在有效循环量子宇宙学中穿着的度量与扰动的混合方法之间的密切关系
On a close relationship between the dressed metric and the hybrid approach to perturbations in effective loop quantum cosmology
论文作者
论文摘要
穿着的度量标准和扰动的混合方法是捕获量子几何形状在环路量子宇宙学中原始功率频谱中量子几何影响的两种主要方法。两者都考虑在循环量化的背景上进行量化的FOCK扰动，并产生非常相似的预测，除了在Planck制度中退出有效时空中的地平线的模式。迄今为止，由于构建和技术假设的差异，了解两种方法之间的精确关系仍然被遮盖了。我们在线性扰动的经典且有效的时空级别上探索了这个问题，而忽略了反应，这是迄今为止两种方法中功率谱的实际计算的水平。我们首先表明，在经典级别，两种方法都导致相同的汉密尔顿人在扰动中达到第二阶，并在物理溶液中在Mukhanov-Sasaki方程中导致相同的经典质量函数。在有效的时空级别上，可以追溯到普朗克政权两种方法之间的现象学预测差异，可以追溯到是否使用Mukhanov-Sasaki可变$ q _ {\ vec k} $（穿着的公制方法）或其重新定制的版本$ n veec k}扰动的哈密顿量和相关的聚合歧义。事实证明，如果在穿着的指标方法中，人们选择与$ν_ {\ vec {k}} $一起使用，则有效的质量函数可以完全像混合方法中一样书写，从而导致所有制度中的现象学预测相同。我们的结果明确表明，在实用的计算水平上，穿着的度量标准和线性扰动的混合方法可以看作是同一硬币的两个方面。
The dressed metric and the hybrid approach to perturbations are the two main approaches to capture the effects of quantum geometry in the primordial power spectrum in loop quantum cosmology. Both consider Fock quantized perturbations over a loop quantized background and result in very similar predictions except for the modes which exit the horizon in the effective spacetime in the Planck regime. Understanding precise relationship between both approaches has so far remained obscured due to differences in construction and technical assumptions. We explore this issue at the classical and effective spacetime level for linear perturbations, ignoring backreaction, which is the level at which practical computations of the power spectrum in both of the approaches have so far been performed. We first show that at the classical level both the approaches lead to the same Hamiltonian up to the second order in perturbations and result in the same classical mass functions in the Mukhanov-Sasaki equation on the physical solutions. At the effective spacetime level, the difference in phenomenological predictions between the two approaches in the Planck regime can be traced to whether one uses the Mukhanov-Sasaki variable $Q_{\vec k}$ (the dressed metric approach) or its rescaled version $ν_{\vec k}=aQ_{\vec k}$ (the hybrid approach) to write the Hamiltonian of the perturbations, and associated polymerization ambiguities. It turns out that if in the dressed metric approach one chooses to work with $ν_{\vec{k}}$, the effective mass function can be written exactly as in the hybrid approach, thus leading to identical phenomenological predictions in all regimes. Our results explicitly show that the dressed metric and the hybrid approaches for linear perturbations, at a practical computational level, can be seen as two sides of the same coin.
