Peak-Background Split, Renormalization, and Galaxy Clustering

TL;DR

This paper derives a rigorous framework for galaxy clustering statistics using the peak-background split, introducing renormalized bias parameters that are physically interpretable and scale-independent, improving upon naive local bias models.

Contribution

It provides a formal derivation of two-point correlations in the PBS framework with renormalized bias parameters, capturing scale-dependent biases and primordial non-Gaussianity effects.

Findings

Bias parameters are physically interpretable and scale-independent.

The formalism naturally predicts scale-dependent bias ~ k^2.

The approach accounts for primordial non-Gaussianity effects.

Abstract

We present a derivation of two-point correlations of general tracers in the peak-background split (PBS) framework by way of a rigorous definition of the PBS argument. Our expressions only depend on connected matter correlators and "renormalized" bias parameters with clear physical interpretation, and are independent of any coarse-graining scale. This result should be contrasted with the naive expression derived from a local bias expansion of the tracer number density with respect to the matter density perturbation \delta_L coarse-grained on a scale R_L. In the latter case, the predicted tracer correlation function receives contributions of order <\delta_L^n> at each perturbative order n, whereas, in our formalism, these are absorbed in the PBS bias parameters at all orders. Further, this approach naturally predicts both a scale-dependent bias ~ k^2 such as found for peaks of the density field, and the scale-dependent bias induced by primordial non-Gaussianity in the initial conditions. The only assumption made about the tracers is that their abundance at a given position depends solely on the matter distribution within a finite region around that position.