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

TL;DR

This paper evaluates the flat-sky approximation for galaxy number counts, demonstrating high accuracy and significant computational speed-up compared to full-sky calculations, especially useful for cosmological analyses.

Contribution

It introduces a semi-analytic method and an improved code implementation that greatly enhances the efficiency of flat-sky approximations in galaxy correlation studies.

Findings

Agreement within 5% for certain contributions at z > 0.5

Agreement within 1% for multipoles at z > 1 and small separations

Flat-sky multipole computation is over 10,000 times faster than full-sky methods

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.