The relativistic galaxy number counts in the weak field approximation

Abstract

We present a novel approach to compute systematically the relativistic projection effects at any order in perturbation theory within the weak field approximation. In this derivation the galaxy number counts is written completely in terms of the redshift perturbation. The relativistic effects break the symmetry along the line-of-sight and they source, contrarily to the standard perturbation theory, the odd multipoles of the matter power spectrum or 2-point correlation function, providing a unique signature for their detection in Large Scale Structure surveys. We show that our approach agrees with previous derivations (up to third order) of relativistic effects and, for the first time, we derive a model for the transverse Doppler effect. Moreover, we show that in the Newtonian limit this approach is consistent with standard perturbation theory at any order.

17 pages, v2: minor modifications to match published version

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Cited by in corpus (15)

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• Testing the equivalence principle on cosmological scales using the odd multipoles of galaxy cross-power spectrum and bispectrum
• Wide-angle effects in the galaxy bispectrum
• The skewness of the distance-redshift relation in $\Lambda$CDM
• Euclid: Relativistic effects in the dipole of the 2-point correlation function
• Nonlinear Redshift-Space Distortions on the Full Sky
• Detecting Relativistic Doppler in Galaxy Clustering with Tailored Galaxy Samples
• Doppler bias: impact of peculiar velocities on color selection and the large scale structure of galaxy surveys
• Detecting Relativistic Doppler by Multi-Tracing a Single Galaxy Population
• Gravitational Redshift from Galaxy Clusters -- a Relativistic Approach
• Detecting Local and Integrated Relativistic Effects by Multi-Tracing a Single Galaxy Population in Harmonic Space
• Gravitational redshift from large-scale structure: nonlinearities, antisymmetries, and the dipole