General relativity (GR) extensions based on renormalization group (RG) flows may lead to scale-dependent couplings with nontrivial effects at large distance scales. Here we develop further the approach in which RG effects at large distance scales are fully encoded in an effective action and we apply it to cosmology. In order to evaluate the cosmological consequences, our main assumption is the use of a RG scale such that the (infrared) RG effects only appear at perturbative order (not at the background level). The emphasis here is on analytical results and qualitative understanding of the implied cosmology. We employ commonly used parametrizations for describing modified gravity in cosmology (as the slip parameter). From them, we describe the dynamics of the first order perturbations and estimate bounds on the single dimensionless parameter (\(\nu \)) introduced by this framework. Possible impacts on dark matter and dark energy are discussed. It is also shown here that the \(\nu \) parameter effects to \(f\sigma _8\) are stronger at low redshifts (\(z<1.5\)), while different values for \(\nu \) do not appreciably change \(f\sigma _8\) at higher redshifts, thus opening a window to alleviate an issue that is currently faced by \(\Lambda \)CDM.

中文翻译：

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重归一化的宇宙学框架在行动层面上扩展了引力

基于重归一化组（RG）流动的广义相对论（GR）扩展可能会导致与尺度相关的耦合，并且在大距离尺度上具有非平凡的影响。在这里，我们进一步发展了一种方法，在该方法中，可以有效地将远距离尺度的RG效应完全编码为有效动作，并将其应用于宇宙学。为了评估宇宙学的后果，我们的主要假设是使用RG量表，以使（红外）RG效应仅以扰动的顺序出现（而不是背景水平）。这里的重点是分析结果和对隐含宇宙学的定性理解。我们采用常用的参数化方法来描述宇宙学中的修正重力（作为滑动参数）。通过它们，我们描述了一阶摄动的动力学，并估计了单个无量纲参数的边界（此框架引入的\（\ nu \））。讨论了对暗物质和暗能量的可能影响。此处还表明，\（\ NU \）参数效果\（F \西格玛_8 \）是在低红移（更强\（Z <1.5 \） ），而不同的值\（\ NU \）做在较高的红移下不会明显地更改\（f \ sigma _8 \），从而为缓解\（\ Lambda \） CDM当前面临的问题打开了一个窗口。