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We show how to obtain constraints on $\beta=f/b$, the ratio of the mattergrowth rate and the bias that quantifies the linear redshift-space distortions,that are independent of the cosmological model, using multiple tracers oflarge-scale structure. For a single tracer the uncertainties on $\beta$ areconstrained by the uncertainties in the amplitude and shape of the powerspectrum, which is limited by cosmic variance. However, for two or more tracersthis limit does not apply, since taking the ratio of power spectra cosmicvariance cancels out, and in the linear (Kaiser) approximation one measuresdirectly 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 analyticformulae for the Fisher matrix for one and two tracers, and quantify thesignal-to-noise ratio needed to make effective use of the multiple-tracertechnique. We also forecast the errors on $\beta$ for a survey like Euclid.

Fisher matrix for multiple tracers: model independent constraints on the redshift distortion parameter