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 $\Lambda$ 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.