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

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 ≲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, 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 simulations for cosmological parameter estimation.