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
$\lesssim 250$ 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.
