We revisit the calculation of quantum-gravitational corrections to the power spectra of scalar and tensor perturbations in the Born-Oppenheimer approach to quantum gravity. We focus on the issue of the definition of the inner product of the theory and the unitarity of the corrections to the dynamics of the cosmological perturbations. We argue that the correction terms are unitary, provided the inner product is defined in a suitable way, which can be related to a notion of gauge fixing the time variable and the use of conditional probabilities in quantum cosmology. We compare the corrections obtained within this framework to earlier results in the literature and we conclude with some remarks on the physical interpretation of the correction terms.

中文翻译：

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量子引力校正对Born-Oppenheimer方法中原始波动的统一性

我们将重新研究Born-Oppenheimer量子引力方法中标量和张量摄动功率谱的量子引力校正计算。我们关注理论的内积定义问题和宇宙扰动动力学校正的统一性。我们认为，校正项是统一的，只要内部产物以合适的方式定义，这可能与确定时间变量的量规概念和量子宇宙学中条件概率的使用有关。我们将在此框架内获得的更正与文献中的较早结果进行比较，并以更正术语的物理解释得出一些结论。