Galaxy number counts at second order: an independent approach

Abstract

Next generation surveys will be capable of determining cosmological parameters beyond percent level. To match this precision, theoretical descriptions should look beyond the linear perturbations to approximate the observables in large scale structure. A quantity of interest is the Number density of galaxies detected by our instruments. This has been focus of interest recently, and several efforts have been made to explain relativistic effects theoretically, thereby testing the full theory. However, the results at nonlinear level from previous works are in disagreement. We present a new and independent approach to computing the relativistic galaxy number counts to second order in cosmological perturbation theory. We derive analytical expressions for the full second order relativistic observed redshift, for the angular diameter distance and for the volume spanned by a survey. Finally, we compare our results with previous works which compute the general distance-redshift relation, finding that our result is in agreement at linear order.

arXiv comment35 pages, 4 figures

References in corpus (24)

• The Baryon Oscillation Spectroscopic Survey of SDSS-III
• Cosmological perturbations
• 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
• General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?
• (Mis-)Interpreting supernovae observations in a lumpy universe
• Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
• Galaxy number counts to second order and their bispectrum
• xPand: An algorithm for perturbing homogeneous cosmologies
• The extended Baryon Oscillation Spectroscopic Survey (eBOSS): a cosmological forecast
• 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 second-order luminosity-redshift relation in a generic inhomogeneous cosmology
• Relativistic Effect in Galaxy Clustering
• Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. I - Key results
• Observed galaxy number counts on the lightcone up to second order: II. Derivation
• Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. II - Derivation
• On the Conformal forms of the Robertson-Walker metric
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
• Unified Treatment of the Luminosity Distance in Cosmology
• Higher order relativistic galaxy number counts: dominating terms
• Fluctuations of differential number counts of radio continuum sources

Cited by in corpus (5)

• Decoupling Local Primordial non-Gaussianity from Relativistic Effects in the Galaxy Bispectrum
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• Observable Gravitational Wave Strain at Second Order
• Visualising relativistic effects in redshift space distortions of large scale structure
• Galaxy number counts at second order in perturbation theory: a leading-order term comparison