N-point correlations of dark matter tracers : Renormalization with univariate biasing and its O(f_{NL}) terms with bivariate biasing

TL;DR

This paper extends a galaxy biasing model to include renormalization of tracer n-point functions, analyzes the impact of non-Gaussianity parameters, and clarifies the behavior of higher-order cumulants.

Contribution

It introduces a renormalization framework for tracer n-point functions in galaxy biasing models and examines the influence of f_{NL} on higher-order correlations.

Findings

4 and higher point cumulants lack O(f_{NL}) terms

All O(f_{NL}) terms in n-point correlations are extracted for bivariate biasing

Extended combinatorial technology for renormalization of biasing models

Abstract

In this note we extend the results of the model of galaxy biasing recently proposed in (http://arxiv.org/abs/1212.0868v2). In that paper the authors had outlined a very precise mathematical framework to deal with the theory of galaxy biasing. In this work we extend that combinatorial technology to renormalize tracer n-point functions in their model of univariate biasing. We further prove that 4 and higher point cumulants of the Bardeen potential don't have an O(f_{NL}) term. Then we use this observation to extract all the O(f_{NL}) terms in the n-point correlation of tracers in their model of bivariate biasing.