The linear power spectrum of observed source number counts

Abstract

We relate the observable number of sources per solid angle and redshift to the underlying proper source density and velocity, background evolution and line-of-sight potentials. We give an exact result in the case of linearized perturbations assuming general relativity. This consistently includes contributions of the source density perturbations and redshift distortions, magnification, radial displacement, and various additional linear terms that are small on sub-horizon scales. In addition we calculate the effect on observed luminosities, and hence the result for sources observed as a function of flux, including magnification bias and radial-displacement effects. We give the corresponding linear result for a magnitude-limited survey at low redshift, and discuss the angular power spectrum of the total count distribution. We also calculate the cross-correlation with the CMB polarization and temperature including Doppler source terms, magnification, redshift distortions and other velocity effects for the sources, and discuss why the contribution of redshift distortions is generally small. Finally we relate the result for source number counts to that for the brightness of line radiation, for example 21-cm radiation, from the sources.

17 pages, 8 figures. Minor changes to match version accepted for PRD. CAMB sources code available at http://camb.info/sources/

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• Interacting Quintessence and Growth of Structure
• Fisher matrix for the angular power spectrum of multi-tracer galaxy surveys
• Infrared Sensitivity of Cosmological Probes in Horndeski Theory
• The large-scale monopole of the power spectrum in a Euclid-like survey: wide-angle effects, lensing, and the `finger of the observer'
• Dark energy and non-linear power spectrum
• Gravitational redshift from large-scale structure: nonlinearities, antisymmetries, and the dipole
• Cosmic Dipoles from Large-Scale Structure Surveys
• Visualising relativistic effects in redshift space distortions of large scale structure
• Detecting Local and Integrated Relativistic Effects by Multi-Tracing a Single Galaxy Population in Harmonic Space
• Prospects for measuring the Doppler magnification dipole with LSST and DESI
• Large-scale Modeling of the Observed Power Spectrum Multipoles
• The BINGO project X. Cosmological parameter constraints from HI Intensity Mapping lognormal simulations
• Improving Photometric Galaxy Clustering Constraints With Cross-Bin Correlations
• Probing beyond-Horndeski gravity on ultra-large scales
• Galaxy number-count dipole and superhorizon fluctuations
• Applications of Cosmological Perturbation Theory in the Late Universe
• Enhancing Bispectrum Estimators for Galaxy Redshift Surveys with Velocities
• Origin & evolution of the Universe
• Improving cosmological covariance matrices with machine learning
• Large scale structures: from inflation to today: a brief report
• Living in a Non-Flat Universe: Theoretical Formalism
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects
• Relativistic Angular Redshift Fluctuations embedded in Large Scale Varying Gravitational Potentials
• Towards simulating a realistic data analysis with an optimised angular power spectrum of spectroscopic galaxy surveys
• Dynamics of tachyon dark energy on large scales and its imprint on observed galaxy power spectrum