A number of radio interferometers are currently being planned or constructed to observe 21 cm emission from reionization .
Not only will such measurements provide a detailed view of that epoch , but , since the 21 cm emission also traces the distribution of matter in the Universe , this signal can be used to constrain cosmological parameters at 6 \lesssim z \lesssim 20 .
The sensitivity of an interferometer to the cosmological information in the signal may depend on how precisely the angular dependence of the 21 cm 3-D power spectrum can be measured .
Utilizing an analytic model for reionization , we quantify all the effects that break the spherical symmetry of the 3-D 21 cm power spectrum and produce physically motivated predictions for this power spectrum .
We find that upcoming observatories will be sensitive to the 21 cm signal over a wide range of scales , from larger than 100 to as small as 1 comoving Mpc .
Next , we consider three methods to measure cosmological parameters from the signal : ( 1 ) direct fitting of the density power spectrum to the signal ( this method can only be applied when density fluctuations dominate the 21 cm fluctuations ) , ( 2 ) using only the velocity field fluctuations in the signal , ( 3 ) looking at the signal at large enough scales such that all fluctuations trace the density field .
With the foremost method , the first generation of 21 cm observations should moderately improve existing constraints on cosmological parameters for certain low-redshift reionization scenarios , and a two year observation with the second generation interferometer MWA5000 in combination with the CMB telescope Planck can improve constraints on \Omega _ { w } ( to \pm 0.017 , a 1.7 times smaller uncertainty than from Planck alone ) , \Omega _ { m } h ^ { 2 } ( \pm 0.0009 , 2.5 times ) , \Omega _ { b } h ^ { 2 } ( \pm 0.00012 , 1.5 times ) , \Omega _ { \nu } ( \pm 0.003 , 3 times ) , n _ { s } ( \pm 0.0033 , 1.4 times ) , and \alpha _ { s } ( \pm 0.003 , 2.7 times ) .
Larger interferometers , such as SKA , have the potential to do even better .
If the Universe is substantially ionized by z \sim 12 or if spin temperature fluctuations are important , we show that it will be difficult to place competitive constraints on cosmological parameters from the 21 cm signal with any of the considered methods .