From matter to galaxies: General relativistic bias for the one-loop bispectrum

TL;DR

This paper develops a relativistic bias expansion framework for the galaxy bispectrum, accounting for non-linear and relativistic effects crucial for accurate primordial non-Gaussianity measurements.

Contribution

It introduces a relativistic Lagrangian bias expansion up to fourth order and demonstrates how to renormalize it to remove unphysical divergences.

Findings

Relativistic bias operators are derived and evolved in time.

Renormalization cancels unphysical divergences in the large-scale bispectrum.

Framework aids in distinguishing primordial signals from relativistic effects.

Abstract

We write down the Lagrangian bias expansion in general relativity up to 4th order in terms of operators describing the curvature of an early-time hypersurface for comoving observers. They can be easily expanded in synchronous or comoving gauges. This is necessary for the computation of the one-loop halo bispectrum, where relativistic effects can be degenerate with a primordial non-Gaussian signal. Since the bispectrum couples scales, an accurate prediction of the squeezed limit behavior needs to be both non-linear and relativistic. We then evolve the Lagrangian bias operators in time in comoving gauge, obtaining non-local operators analogous to what is known in the Newtonian limit. Finally, we show how to renormalize the bias expansion at an arbitrary time and find that this is crucial in order to cancel unphysical $1/k^2$ divergences in the large-scale power spectrum and bispectrum that could be mistaken for a contamination to the non-Gaussian signal.