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

TL;DR

This paper extends the renormalization group framework for large-scale structure to include stochastic effects, deriving equations that describe how stochasticity and bias evolve with scale, impacting cosmological data analysis.

Contribution

It introduces a comprehensive RG approach incorporating stochastic contributions at all orders, revealing how stochastic moments are generated and evolve from bias terms.

Findings

Single nonlinear bias generates all stochastic moments through RG evolution.

Stochastic evolution is governed by a lower scale than the nonlinear scale.

Implications for optimal renormalization scale in cosmological data analysis.

Abstract

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.