LAUSR

We study the flat-sky approximation for galaxy number counts including relativistic effects, and numerically 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,[Available at https://github.com/JCGoran/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.