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.
