Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole

Abstract

We present a fully non-linear and relativistically covariant expression for the observed galaxy density contrast. Building on a null tetrad tailored to the cosmological observer's past light cone, we find a decomposition of the non-linear galaxy over-density into manifestly gauge-invariant quantities, each of which has a clear physical interpretation as a cosmological observable. This ensures that the monopole of the galaxy over-density field (the mean galaxy density as a function of observed redshift) is properly accounted for. We anticipate that this decomposition will be useful for future work on non-linearities in galaxy number counts, for example, deriving the relativistic expression for the galaxy bispectrum. We then specialise our results to conformal Newtonian gauge, with a Hubble parameter either defined globally or measured locally, illustrating the significance of the different contributions to the observed monopole of the galaxy density.

(v1) Comments welcome. (v2) Updated to agree with version accepted to JCAP; typos fixed

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Cited by in corpus (6)

• Large Scale Limit of the Observed Galaxy Power Spectrum
• Second-order gauge-invariant formalism for the cosmological observables: Complete verification of their gauge-invariance
• Gauge invariance on the light-cone: curvature perturbations and radiative degrees of freedom
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• A Simple, Exact Formulation of Number Counts in the Geodesic-Light-Cone Gauge
• The gauge invariant cosmological Jacobi map from weak lensing at leading order