The flat-sky approximation to galaxy number counts -- redshift space correlation function

Abstract

We study the flat-sky approximation for galaxy number counts including relativistic effects, and assess its performance and accuracy with respect to the full-sky result. We find an agreement of up to 5% for the local and lensing contributions to the 2-point correlation function and its multipoles at $z>0.5$, and up to 1% for the multipoles alone at $z>1$ and separations $\lesssim 250$ Mpc/$h$, with a speed-up of over a factor of 1000. Using a semi-analytic method, which has been implemented in a new version of the code COFFE, along with the Limber approximation for the integrated contributions, we further increase the performance, allowing the computation of the flat-sky multipoles to be done over 10000 times faster than in the full-sky calculation, which could be used to greatly speed-up Markov chain Monte Carlo sampling for cosmological parameter estimation.

arXiv comment32 pages, 8 figures. Fixed missing factor of 2 in density-lensing eq. (2.15). Code available at https://github.com/JCGoran/coffe

References in corpus (27)

• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• Euclid Definition Study Report
• Large-Scale Galaxy Bias
• The linear power spectrum of observed source number counts
• What galaxy surveys really measure
• Extended Limber Approximation
• An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Uncorrelated Modes of the Nonlinear Power Spectrum
• Fast and reliable MCMC for cosmological parameter estimation
• Searching for modified growth patterns with tomographic surveys
• Euclid preparation: II. The EuclidEmulator -- A tool to compute the cosmology dependence of the nonlinear matter power spectrum
• Extending cosmological tests of General Relativity with the Square Kilometre Array
• The effect of Limber and flat-sky approximations on galaxy weak lensing
• The full-sky relativistic correlation function and power spectrum of galaxy number counts: I. Theoretical aspects
• Optimising the measurement of relativistic distortions in large-scale structure
• On the importance of lensing for galaxy clustering in photometric and spectroscopic surveys
• The Generation of Vorticity in Cosmological N-body Simulations
• COFFE: a code for the full-sky relativistic galaxy correlation function
• 2-FAST: Fast and accurate computation of projected two-point functions
• Cosmological ensemble and directional averages of observables
• Unequal-Time Correlators for Cosmology
• Unequal time correlators and the Zeldovich approximation
• CMB spectra and bispectra calculations: making the flat-sky approximation rigorous
• The Flat Sky Approximation to Galaxy Number Counts

Cited by in corpus (5)

• The observed galaxy power spectrum in General Relativity
• Large Scale Limit of the Observed Galaxy Power Spectrum
• Small scale effects in the observable power spectrum at large angular scales
• Relativistic imprints on dispersion measure space distortions
• Impact of lensing magnification on the analysis of galaxy clustering in redshift space