Constraints on the growth rate using the observed galaxy power spectrum

The large-scale structure growth index $\gamma$ provides a consistency test of the standard cosmology and is a potential indicator of modified gravity. We investigate the constraints on $\gamma$ from next-generation spectroscopic surveys, using the power spectrum that is observed in redshift space, i.e., the angular power spectrum. The angular power spectrum avoids the need for an Alcock-Packzynski correction. It also naturally incorporates cosmic evolution and wide-angle effects, without any approximation. We include the cross-correlations between redshift bins, using a hybrid approximation when the total number of bins is computationally unfeasible. We show that the signal-to-noise on $\gamma$ increases as the redshift bin-width is decreased. Noise per bin also increases -- but this is compensated by the increased number of auto- and cross-spectra. In our forecasts, we marginalise over the amplitude of primordial fluctuations and other standard cosmological parameters, including the dark energy equation of state parameter, as well as the clustering bias. Neglecting cross-bin correlations increases the errors by $\sim40 - 150\%$. Using only linear scales, we find that a DESI-like BGS survey and an HI intensity mapping survey with the SKA1 precursor MeerKAT deliver similar errors of $\sim4-6\%$, while a Euclid-like survey and an SKA1 intensity mapping survey give $\sim3\%$ errors.