The effective approach in loop quantum cosmology (LQC) has provided means to obtain predictions for observable quantities in LQC models. While an effective dynamics in LQC has been extensively considered in different scenarios, a robust demonstration of the validity of effective descriptions for the perturbative level still requires further attention. The consistency of the description adopted in most approaches requires the assumption of a test field approximation, which is limited to the cases in which the backreaction of the particles gravitationally produced can be safely neglected. Within the framework of LQC, some of the main approaches to quantize the linear perturbations are the dressed metric, the hybrid approaches and the closed or deformed algebra approach. Here, we analyze the consistency of the test field assumption in these frameworks by computing the energy density stored in the particles gravitationally produced compared to the background energy density. This analysis ultimately provides us with a consistency test of the effective descriptions of LQC.

中文翻译：

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引力粒子产生和环量子宇宙学中有效描述的有效性

环量子宇宙学 (LQC) 中的有效方法为获得 LQC 模型中可观测量的预测提供了手段。虽然 LQC 中的有效动力学已在不同场景中得到广泛考虑，但仍需要进一步关注有效描述对微扰水平的有效性的有力证明。大多数方法中采用的描述的一致性需要假设测试场近似，这仅限于可以安全地忽略重力产生的粒子的反向反应的情况。在 LQC 的框架内，量化线性扰动的一些主要方法是修整度量、混合方法和封闭或变形代数方法。这里，我们通过计算存储在重力产生的粒子中的能量密度与背景能量密度相比，分析了这些框架中测试场假设的一致性。这一分析最终为我们提供了对车链有效描述的一致性检验。