Large-scale clustering of galaxies in general relativity

TL;DR

This paper investigates how relativistic effects influence the observed galaxy clustering on large scales near the horizon, deriving gauge-invariant relations and quantifying corrections relevant for cosmological surveys.

Contribution

It derives a gauge-invariant expression for galaxy density perturbations, clarifies gauge dependence in large-scale clustering, and quantifies relativistic corrections comparable to local non-Gaussian bias.

Findings

Relativistic effects cause corrections similar to an effective fNL < 0.5.

Galaxy power spectrum depends strongly on gauge choice near the horizon.

Synchronous-comoving gauge simplifies the relation between galaxy and matter perturbations.

Abstract

Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating galaxy density perturbations to matter density perturbations on large scales, and show that it reduces to a linear bias relation in synchronous-comoving gauge, corroborating an assumption made in several recent papers. We evaluate the resulting observed galaxy power spectrum, and show that it leads to corrections similar to an effective non-Gaussian bias corresponding to a local (effective) fNL < 0.5. This number can serve as a guideline as to which surveys need to take into account relativistic effects. We also discuss the scale-dependent bias induced by primordial non-Gaussianity in the relativistic context, which again is simplest in synchronous-comoving gauge.