Reducing the Variance of Redshift Space Distortion Measurements from
  Mock Galaxy Catalogues with Different Lines of Sight
  Accurate mock catalogues are essential for assessing systematics in the
cosmological analysis of large galaxy surveys. Anisotropic two-point clustering
measurements from the same simulation show some scatter for different lines of
sight (LOS), but are on average equal, due to cosmic variance. This results in
scatter in the measured cosmological parameters. We use the OuterRim N-body
simulation halo catalogue to investigate this, considering the 3 simulation
axes as LOS. The quadrupole of the 2-point statistics is particularly sensitive
to changes in the LOS, with sub-percent level differences in the velocity
distributions resulting in ~1.5$\sigma$ shifts on large scales. Averaging over
multiple LOS can reduce the impact of cosmic variance. We derive an expression
for the Gaussian cross-covariance between the power spectrum multipole
measurements, for any two LOS, including shot noise, and the corresponding
reduction in variance in the average measurement. Quadrupole measurements are
anti-correlated, and for three orthogonal LOS, the variance on the average
measurement is reduced by more than 1/3. We perform a Fisher analysis to
predict the corresponding gain in precision on the cosmological parameter
measurements, which we compare against a set of 300 extended Baryon Oscillation
Spectroscopic Survey (eBOSS) emission line galaxy (ELG) EZmocks. The gain in
$f\sigma_8$, which measures the growth of structure, is also better than 1/3.
Averaging over multiple LOS in future mock challenges will allow the RSD models
to be constrained with the same systematic error, with less than 3 times the
CPU time.
