Constraining the growth rate by combining multiple future surveys

The growth rate of large-scale structure provides a powerful consistency test of the standard cosmological model and a probe of possible deviations from general relativity. We use a Fisher analysis to forecast constraints on the growth rate from a combination of next-generation spectroscopic surveys. In the overlap survey volumes, we use a multi-tracer analysis to significantly reduce the effect of cosmic variance. The non-overlap individual survey volumes are included in the Fisher analysis in order to utilise the entire volume. We use the observed angular power spectrum, which naturally includes all wide-angle and lensing effects and circumvents the need for an Alcock-Paczynski correction. Cross correlations between redshift bins are included by using a novel technique to avoid computation of the sub-dominant contributions. Marginalising over the standard cosmological parameters, as well as the clustering bias in each redshift bin, we find that the precision on $\gamma$ improves on the best single-tracer precision by up to $\sim$50\%.