Optimal Weighting in Galaxy Surveys: Application to Redshift-Space
  Distortions
  Using multiple tracers of large-scale structure allows to evade the
limitations imposed by sampling variance for some parameters of interest in
cosmology. We demonstrate the optimal way of carrying out a multitracer
analysis in a galaxy redshift survey by considering the principal components of
the shot noise matrix from two-point clustering statistics. We show how to
construct two tracers that maximize the benefits of sampling variance and shot
noise cancellation using optimal weights. On the basis of high-resolution
N-body simulations of dark matter halos we apply this technique to the analysis
of redshift-space distortions and demonstrate how constraints on the growth
rate of structure formation can be substantially improved. The primary
limitation are nonlinear effects, which cause significant biases in the method
already at scales of k<0.1h/Mpc, suggesting the need to develop nonlinear
models of redshift-space distortions in order to extract the maximum
information from future redshift surveys. Nonetheless we find gains of a factor
of a few in constraints on the growth rate achievable when merely the linear
regime of a galaxy survey like EUCLID is considered.
