标题： 在衣着度规与有效环量子宇宙学中扰动的混合方法之间的紧密关系 显示英文标题

标题： On a close relationship between the dressed metric and the hybrid approach to perturbations in effective loop quantum cosmology

摘要： 有质量度规和摄动的混合方法是圈量子宇宙学中捕捉原初功率谱中量子几何效应的两种主要方法。 两者都考虑在圈量子背景上进行福克量子化摄动，并且除了在普朗克尺度的有效时空中退出视界的模式外，结果非常相似。 由于构造和技术假设的不同，至今尚未明确理解这两种方法之间的精确关系。 我们探讨了在经典和有效时空层面上线性摄动的问题，忽略了反作用，这是目前在这两种方法中进行功率谱实际计算的层面。 我们首先表明，在经典层面上，这两种方法在摄动的二阶以内导致相同的哈密顿量，并在物理解上产生相同的经典质量函数，即 Mukhanov-Sasaki 方程中的质量函数。 在有效时空层面上，两种方法在普朗克尺度上的现象学预测差异可以追溯到是否使用 Mukhanov-Sasaki 变量$Q_{\vec k}$（有质量度规方法）或其缩放版本$\nu_{\vec k}=aQ_{\vec k}$（混合方法）来写出摄动的哈密顿量，以及相关的聚合化歧义。 结果表明，如果在有质量度规方法中选择使用$\nu_{\vec{k}}$，则有效质量函数可以精确地写成与混合方法相同的形式，从而在所有尺度上产生相同的现象学预测。 我们的结果明确显示，在实际计算层面上，有质量度规方法和混合方法对于线性摄动可以被视为同一硬币的两面。 显示英文摘要

摘要： 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 $\nu_{\vec k}=aQ_{\vec k}$ (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 $\nu_{\vec{k}}$, 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.