Scale-dependent bias from primordial non-Gaussianity in general relativity

TL;DR

This paper investigates how primordial non-Gaussianity affects scale-dependent bias within general relativity, confirming that relativistic corrections are negligible on large scales and discussing implications for correlation functions.

Contribution

It justifies the use of the Poisson equation in relativistic perturbation theory for bias derivation and clarifies the scale dependence of bias without relativistic corrections.

Findings

Relativistic corrections to scale-dependent bias are negligible on super-Hubble scales.

The form of bias remains consistent with Newtonian predictions in general relativity.

Correlation functions for biased tracers diverge formally, requiring careful interpretation.

Abstract

In this note we examine the derivation of scale-dependent bias due to primordial non-Gaussianity of the local type in the context of general relativity. We justify the use of the Poisson equation in general relativistic perturbation theory and thus the derivation of scale-dependent bias as a test of primordial non-Gaussianity, using the spherical collapse model. The corollary is that the form of scale-dependent bias does not receive general relativistic corrections on scales larger than the Hubble radius. This leads to a formally divergent correlation function for biased tracers of the mass distribution which we discuss.