It was recently shown that the volume operator of loop quantum cosmology (LQC) and all its positive powers are ill-defined on physical states. In this paper, we investigate how it effects predictions of cosmic microwave background (CMB) power spectra obtained within dressed metric approach for which expectations values of $\hat{a}$ are the key element. We find that almost every step in the procedure is ill-defined and relies heavily upon a (seemingly premature) numerical truncation. Thus, it suggests that more care is needed in making predictions regarding pre-inflationary physics. We propose a new scheme which contains only well-defined quantities. The surprising agreement of the hitherto models with observational data, especially at low angular momenta $l$ is explained.

中文翻译：

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重新审视着装指标预测

最近表明，环量子宇宙学 (LQC) 的体积算符及其所有正幂在物理状态上是不明确的。在本文中，我们研究了它如何影响在修饰度量方法中获得的宇宙微波背景 (CMB) 功率谱的预测，其中 $\hat{a}$ 的期望值是关键元素。我们发现该过程中的几乎每一步都定义不明确，并且严重依赖（似乎为时过早的）数值截断。因此，它表明在预测暴胀前物理学时需要更加谨慎。我们提出了一个只包含明确定义的数量的新方案。解释了迄今为止模型与观测数据的惊人一致性，尤其是在低角动量 $l$ 时。