Optimal Weights For Measuring Redshift Space Distortions in Multi-tracer
  Galaxy Catalogues
  Since the volume accessible to galaxy surveys is fundamentally limited, it is
extremely important to analyse available data in the most optimal fashion. One
way of enhancing the cosmological information extracted from the clustering of
galaxies is by weighting the galaxy field. The most widely used weighting
schemes assign weights to galaxies based on the average local density in the
region (FKP weights) and their bias with respect to the dark matter field (PVP
weights). They are designed to minimize the fractional variance of the galaxy
power-spectrum. We demonstrate that the currently used bias dependent weighting
scheme can be further optimized for specific cosmological parameters. We
develop a procedure for computing the optimal weights and test them against
mock catalogues for which the values of all fitting parameters, as well as the
input power-spectrum are known. We show that by applying these weights to the
joint power-spectrum of Emission Line Galaxies and Luminous Red Galaxies from
the Dark Energy Spectroscopic Instrument survey, the variance in the measured
growth rate parameter can be reduced by as much as 36 per cent.
