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.

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

References in corpus (50)

• Weak Gravitational Lensing
• A 2.4% Determination of the Local Value of the Hubble Constant
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Large-Scale Galaxy Bias
• The linear power spectrum of observed source number counts
• What galaxy surveys really measure
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Large-scale clustering of galaxies in general relativity
• Fluctuations of the luminosity distance
• Cosmology with the SPHEREX All-Sky Spectral Survey
• Single-Field Consistency Relations of Large Scale Structure
• Symmetries and Consistency Relations in the Large Scale Structure of the Universe
• Cosmic variance and the measurement of the local Hubble parameter
• Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure
• Light-cone averaging in cosmology: formalism and applications
• The effect of peculiar velocities on supernova cosmology
• Light Propagation in Arbitrary Spacetimes and the Gravitational Lens Approximation
• Cosmic Rulers
• Beyond the plane-parallel and Newtonian approach: Wide-angle redshift distortions and convergence in general relativity
• Galaxy number counts to second order and their bispectrum
• The Correlation Function in Redshift Space: General Formula with Wide-angle Effects and Cosmological Distortions
• On Separate Universes
• Observed galaxy number counts on the lightcone up to second order: I. Main result
• An exact Jacobi map in the geodesic light-cone gauge
• The bispectrum of relativistic galaxy number counts
• The observed galaxy power spectrum in General Relativity
• Large-Scale Bulk Motions Complicate the Hubble Diagram
• All-Sky Analysis of the General Relativistic Galaxy Power Spectrum
• Multipole decomposition of the general luminosity distance 'Hubble law' -- a new framework for observational cosmology
• Large-scale 3D galaxy correlation function and non-Gaussianity
• Finite Source Effects in Strong Lensing: Implications for the Substructure Mass Scale
• The Gravitational Lensing in Redshift-space Correlation Functions of Galaxies and Quasars
• Large-Scale Structure Observables in General Relativity
• Consistency of the local Hubble constant with the cosmic microwave background
• A Consistency Relation for the Observed Galaxy Bispectrum and the Local non-Gaussianity from Relativistic Corrections
• A new approach to the propagation of light-like signals in perturbed cosmological backgrounds
• Lensing Corrections to Features in the Angular Two-Point Correlation Function and Power Spectrum
• Gauge-Invariance and Infrared Divergences in the Luminosity Distance
• A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone
• Geodesic-light-cone coordinates and the Bianchi I spacetime
• Deciphering cosmological information from redshift surveys of high-z objects - the cosmological light-cone effect and redshift-space distortion -
• Galaxy Power Spectrum in General Relativity
• Light propagation in inhomogeneous and anisotropic cosmologies
• The Effect of Weak Lensing on the Angular Correlation Function of Faint Galaxies
• Weak gravitational lensing of finite beams
• Non-linear general relativistic effects in the observed redshift
• Cosmic Clocks
• Cutting out the cosmological middle man: General Relativity in the light-cone coordinates
• Generalisation of the Kaiser Rocket effect in general relativity in the wide-angle galaxy 2-point correlation function
• Statistics of a single sky: constrained random fields and the imprint of Bardeen potentials on galaxy clustering

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• 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