Cosmological constraints from multiple tracers in spectroscopic surveys

Abstract: We use the Fisher matrix formalism to study the expansion and growth history of the Universe using galaxy clustering with 2D angular cross-correlation tomography in spectroscopic or high resolution photometric redshift surveys. The radial information is contained in the cross correlations between narrow redshift bins. We show how multiple tracers with redshift space distortions cancel sample variance and arbitrarily improve the constraints on the dark energy equation of state $\omega(z)$ and the growth parameter $\gamma$ in the noiseless limit. The improvement for multiple tracers quickly increases with the bias difference between the tracers, up to a factor $\sim4$ in $\text{FoM}<em>{\gamma\omega}$. We model a magnitude limited survey with realistic density and bias using a conditional luminosity function, finding a factor 1.3-9.0 improvement in $\text{FoM}</em>{\gamma\omega}$ -- depending on global density -- with a split in a halo mass proxy. Partly overlapping redshift bins improve the constraints in multiple tracer surveys a factor $\sim1.3$ in $\text{FoM}_{\gamma\omega}$. This findings also apply to photometric surveys, where the effect of using multiple tracers is magnified. We also show large improvement on the FoM with increasing density, which could be used as a trade-off to compensate some possible loss with radial resolution.