The hybrid and the dressed metric formalisms for the study of primordial perturbations in Loop Quantum Cosmology lead to dynamical equations for the modes of these perturbations that are of a generalized harmonic-oscillator type, with a mass that depends on the background but is the same for all modes. For quantum background states that are peaked on trajectories of the effective description of Loop Quantum Cosmology, the main difference between the two considered formalisms is found in the expression of this mass. The value of the mass at the bounce is especially important, since it is only in a short interval around this event that the quantum geometry effects on the perturbations are relevant. In a previous article, the properties of this mass were discussed for an inflaton potential of quadratic form, or with similar characteristics. In the present work, we extend this study to other interesting potentials in cosmology, namely the Starobinsky and the exponential potentials. We prove that there exists a finite interval of values of the potential (which includes the zero but typically goes beyond the sector of kinetically dominated inflaton energy density) for which the hybrid mass is positive at the bounce whereas the dressed metric mass is negative.

中文翻译：

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Starobinsky 和指数势的环量子宇宙学的混合和修饰度量形式中的宇宙学扰动质量

用于研究环路量子宇宙学中的原始扰动的混合和修饰度量形式导致这些扰动模式的动力学方程属于广义谐波振荡器类型，其质量取决于背景，但对于所有模式。对于在有效描述环量子宇宙学的轨迹上达到峰值的量子背景状态，两种考虑的形式之间的主要区别在于该质量的表达。反弹时的质量值尤其重要，因为仅在该事件前后的很短的时间间隔内，量子几何对扰动的影响才是相关的。在之前的文章中，针对二次形式或具有类似特征的暴胀势讨论了该质量的性质。在目前的工作中，我们将这项研究扩展到宇宙学中其他有趣的势，即 Starobinsky 和指数势。我们证明存在一个有限的势值区间（包括零，但通常超出动力学主导的暴胀能量密度区域），其中混合质量在反弹时为正，而修整的公制质量为负。