Forecasts for dark energy measurements with future H i surveys

We use two independent methods to forecast the dark energy measurements achievable by combining future galaxy redshift surveys based on the radio H i emission line with cosmic microwave background (CMB) data from the Planck satellite. In the first method, we focus on the 'standard ruler' provided by the baryon acoustic oscillation (BAO) length-scale. In the second method, we utilize additional information encoded in the galaxy power spectrum including galaxy bias from velocity-space distortions and the growth of cosmic structure. We find that a radio synthesis array with about 10 per cent of the collecting area of the Square Kilometre Array (SKA), equipped with a wide (10-100 deg2) field of view, would have the capacity to perform a 20 000 deg2 redshift survey to a maximum redshift z(max) similar to 0.8 and thereby produce dark energy measurements that are competitive with surveys likely to be undertaken by optical telescopes around 2015. There would then be powerful arguments for adding collecting area to such a 'Phase 1' SKA because of the square-law scaling of survey speed with telescope sensitivity for H i surveys, compared to the linear scaling for optical redshift surveys. The full SKA telescope should, by performing a 20 000 deg2 H i redshift survey to z(max) similar to 2 around 2020, yield an accurate measurement of cosmological parameters independent of CMB data sets. Combining CMB (Planck) and galaxy power spectrum (SKA) measurements will drive errors in the dark energy equation-of-state parameter w well below the 1 per cent level. The major systematic uncertainty in these forecasts is the lack of direct information about the mass function of high-redshift H i-emitting galaxies. 'Stacking experiments' with SKA pathfinders will play an important role in resolving this uncertainty.