  Galaxy redshift surveys using optical telescopes have, in combination with
other cosmological probes, enabled precision measurements of the nature of dark
energy. We show that radio telescopes are rapidly becoming competitive with
optical facilities in spectroscopic surveys of large numbers of galaxies. Two
breakthroughs are driving this change. Firstly, individual radio telescopes are
more efficient at mapping the sky thanks to the large field-of-view of new
phased-array feeds. Secondly, ever more dishes can be correlated in a
cost-effective manner with rapid increases in computing power. The next decade
will see the coming of age of the 21cm radio wavelength as a cosmological probe
as first the Pathfinders then, ultimately, the Square Kilometre Array is
constructed. The latter will determine precise 3D positions for a billion
galaxies, mapping the distribution of matter in the Universe over the last 12
billion years. This radio telescope will be able to constrain the equation of
state of dark energy, and its potential evolution, to a precision rivalling
that of future optical facilities such as DESI and Euclid.

Cosmology and Nongalactic Astrophysics