The observed galaxy power spectrum in General Relativity

TL;DR

This paper calculates the galaxy power spectrum in Fourier space within General Relativity, demonstrating that all relativistic effects, including lensing and IR divergences, cancel out in observable quantities, providing a baseline for future cosmological studies.

Contribution

It provides the first comprehensive relativistic calculation of the galaxy power spectrum estimator, including all GR effects and arbitrary survey selection functions, clarifying IR divergence issues.

Findings

Relativistic effects are generally small, less than 10% of redshift space distortions.

All IR divergences cancel out when all GR terms are included, due to the Weinberg adiabatic mode.

The work establishes a baseline for analyzing primordial non-Gaussianities with relativistic corrections.

Abstract

Measurements of the clustering of galaxies in Fourier space, and at low wavenumbers, offer a window into the early Universe via the possible presence of scale dependent bias generated by Primordial Non Gaussianites. On such large scales a Newtonian treatment of density perturbations might not be sufficient to describe the measurements, and a fully relativistic calculation should be employed. The interpretation of the data is thus further complicated by the fact that relativistic effects break statistical homogeneity and isotropy and are potentially divergent in the Infra-Red (IR). In this work we compute for the first time the ensemble average of the most used Fourier space estimator in spectroscopic surveys, including all general relativistic (GR) effects, and allowing for an arbitrary choice of angular and radial selection functions. We show that any observable is free of IR sensitivity once all the GR terms, individually divergent, are taken into account, and that this cancellation is a consequence of the presence of the Weinberg adiabatic mode as a solution to Einstein's equations. We then study the importance of GR effects, including lensing magnification, in the interpretation of the galaxy power spectrum multipoles, finding that they are in general a small, less than ten percent level, correction to the leading redshift space distortions term. This work represents the baseline for future investigations of the interplay between Primordial Non Gaussianities and GR effects on large scales and in Fourier space.