# Constraints on the growth rate using the observed galaxy power spectrum

## TL;DR

This paper explores how future galaxy surveys can constrain the growth rate of cosmic structures through the angular power spectrum, accounting for effects like cosmic evolution and wide-angle corrections, to test standard cosmology and modified gravity.

## Contribution

It introduces a method to forecast constraints on the growth index using the angular power spectrum, including cross-correlations and wide-angle effects, improving upon previous approaches.

## Key findings

- Higher redshift bin resolution improves constraints on gamma.
- Cross-bin correlations significantly reduce errors.
- Upcoming surveys can measure gamma with 3-6% precision.

## Abstract

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.