We discuss the possibility of performing a substantial spectroscopic galaxy redshift survey selected via the 21cm emission from neutral hydrogen using the Five-hundred metre Aperture Spherical Telescope (FAST) to be built in China. We consider issues related to the estimation of the source counts and optimizations of the survey, and discuss the constraints on cosmological models that such a survey could provide. We find that a survey taking around two years could detect ~10^7 galaxies with an average redshift of ~0.15 making the survey complementary to those already carried out at optical wavelengths. These conservative estimates have used the z=0 HI mass function and have ignored the possibility of evolution. The results could be used to constrain Gamma = (Omega_m h) to 5 per cent and the spectral index, n_s, to 7 per cent independent of cosmic microwave background data. If we also use simulated power spectra from the Planck satellite, we can constrain w to be within 5 per cent of -1.
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