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The Square Kilometer Array (SKA) has the potential to produce galaxy redshiftsurveys which will be competitive with other state of the art cosmologicalexperiments in the next decade. In this chapter we summarise what capabilitiesthe first and the second phases of the SKA will be able to achieve in itscurrent state of design. We summarise the different cosmological experimentswhich are outlined in further detail in other chapters of this Science Book.The SKA will be able to produce competitive Baryonic Oscillation (BAOs)measurements in both its phases. The first phase of the SKA will providesimilar measurements as optical and IR experiments with completely differentsystematic effects whereas the second phase being transformational in terms ofits statistical power. The SKA will produce very accurate Redshift SpaceDistortions (RSD) measurements, being superior to other experiments at lowerredshifts, due to the large number of galaxies. Cross correlations of thegalaxy redshift data from the SKA with radio continuum surveys and opticalsurveys will provide extremely good calibration of photometric redshifts aswell as extremely good bounds on modifications of gravity. Basing on aPrinciple Component Analysis (PCA) approach, we find that the SKA will be ableto provide competitive constraints on dark energy and modified gravity models.Due to the large area covered the SKA it will be a transformational experimentin measuring physics from the largest scales such as non-Gaussian signals from$\textrm{f}_{\textrm{nl}}$. Finally, the SKA might produce the first real timemeasurement of the redshift drift. The SKA will be a transformational machinefor cosmology as it grows from an early Phase 1 to its full power.

Cosmology from HI galaxy surveys with the SKA