The Renormalization Group for Large-Scale Structure: Primordial non-Gaussianities

TL;DR

This paper extends the renormalization group framework for large-scale structure to include primordial non-Gaussianities, deriving equations that describe how these non-Gaussian effects evolve with scale in galaxy clustering.

Contribution

It introduces interaction vertices for primordial non-Gaussianity into the RG-LSS framework, including new operators and bias coefficients for a comprehensive treatment.

Findings

Recovered scale-dependent bias contributions

Identified a new stochastic contribution

Derived RG equations for non-Gaussian effects

Abstract

The renormalization group for large-scale structure (RG-LSS) describes the evolution of galaxy bias and stochastic parameters as a function of the cutoff $\Lambda$. In this work, we introduce interaction vertices that describe primordial non-Gaussianity into the Wilson-Polchinski framework, thereby extending the free theory to the interacting case. The presence of these interactions forces us to include new operators and bias coefficients to the bias expansion to ensure closure under renormalization. We recover the previously-derived ``scale-dependent bias'' contributions, as well as a new (subdominant) stochastic contribution. We derive the renormalization group equations governing the RG-LSS for a large class of interactions which account for vertices at linear order in $f_{\rm NL}$ that parametrize interacting scalar and massive spinning fields during inflation. Solving the RG equations, we show the evolution of the non-Gaussian contributions to galaxy clustering as a function of scale.