The renormalization group equations for large-scale structure (RG-LSS) describe how the bias and stochastic (noise) parameters — both of matter and biased tracers such as galaxies — evolve as a function of the cutoff Λ of the effective field theory. In previous work, we derived the RG-LSS equations for the bias parameters using the Wilson-Polchinski framework. Here, we extend these results to include stochastic contributions, corresponding to terms in the effective action that are higher order in the current J. We derive the general local interaction terms that describe stochasticity at all orders in perturbations, and a closed set of nonlinear RG equations for their coefficients. These imply that a single nonlinear bias term generates all stochastic moments through RG evolution. Further, the evolution is controlled by a different, lower scale than the nonlinear scale. This has implications for the optimal choice of the renormalization scale when comparing the theory with data to obtain cosmological constraints.

中文翻译：

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大尺度结构的重整化群：星系随机性的起源


大规模结构的重整化群方程 （RG-LSS） 描述了物质和偏置示踪剂（如星系）的偏置和随机（噪声）参数如何演变为有效场论的截止 Λ 的函数。在以前的工作中，我们使用 Wilson-Polchinski 框架推导出了偏置参数的 RG-LSS 方程。在这里，我们将这些结果扩展到包括随机贡献，对应于有效动作中当前 J 中高阶的项。我们推导出了描述扰动中所有阶次的随机性的一般局部交互项，以及一组封闭的非线性 RG 方程作为其系数。这意味着单个非线性偏置项通过 RG 演化生成所有随机矩。此外，演化由与非线性标度不同的、更低的标度控制。这在将理论与数据进行比较以获得宇宙学约束时，对重整化尺度的最佳选择具有影响。