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

TL;DR

The paper investigates whether general relativity modifies the scale-dependent bias from local primordial non-Gaussianity on very large scales. It develops a GR-focused treatment of the Poisson equation and uses spherical collapse to connect density perturbations to biased tracers, highlighting gauge choices (comoving-orthogonal vs longitudinal) and showing that, in the comoving-orthogonal gauge, the Newtonian form of the Poisson equation suffices on all scales, so the leading $k^{-2}$ bias correction remains GR-free for super-Hubble modes. A formal IR divergence in the correlation function emerges from the bias term, but observables remain finite because survey windowing subtracts the mean, with $\tilde{\xi}(r)=\xi(r)-\sigma_W^2$; for finite windows, the divergence is regulated. The results reinforce using standard Newtonian bias prescriptions within GR for current cosmological data and clarify gauge-related subtleties that can appear in the longitudinal gauge.

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.