Fisher matrix for multiple tracers: model independent constraints on the
  redshift distortion parameter
  We show how to obtain constraints on $\beta=f/b$, the ratio of the matter
growth rate and the bias that quantifies the linear redshift-space distortions,
that are independent of the cosmological model, using multiple tracers of
large-scale structure. For a single tracer the uncertainties on $\beta$ are
constrained by the uncertainties in the amplitude and shape of the power
spectrum, which is limited by cosmic variance. However, for two or more tracers
this limit does not apply, since taking the ratio of power spectra cosmic
variance cancels out, and in the linear (Kaiser) approximation one measures
directly the quantity $(1+ \beta_1 \mu^2)^2/(1+ \beta_2 \mu^2)^2$, where $\mu$
is the angle of a given mode with the line of sight. We provide analytic
formulae for the Fisher matrix for one and two tracers, and quantify the
signal-to-noise ratio needed to make effective use of the multiple-tracer
technique. We also forecast the errors on $\beta$ for a survey like Euclid.
