The Renormalization Group for Large-Scale Structure: Origin of Galaxy Stochasticity

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 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 show that the RG equations exhibit an interesting, previously unnoticed structure at all orders in J, which implies that a single nonlinear bias term immediately generates all stochastic moments through RG evolution. We then derive the nonlinear RG evolution of the (leading-derivative) stochastic parameters for all n-point functions, and show that this 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.