21cm emission from residual neutral hydrogen after the epoch of reionization can be used to trace the cosmological power spectrum of density fluctuations. Using a Fisher matrix formulation, we provide a detailed forecast of the constraints on cosmological parameters that are achievable with this probe. We consider two designs: a scaled-up version of the MWA observatory as well as a Fast Fourier Transform Telescope. We find that 21cm observations dedicated to post-reionization redshifts may yield significantly better constraints than next generation Cosmic Microwave Background (CMB) experiments. We find the constraints on $Omega_Lambda$, $Omega_{rm m}h^2$, and $Omega_ u h^2$ to be the strongest, each improved by at least an order of magnitude over the Planck CMB satellite alone for both designs. Our results do not depend as strongly on uncertainties in the astrophysics associated with the ionization of hydrogen as similar 21cm surveys during the epoch of reionization. However, we find that modulation of the 21cm power spectrum from the ionizing background could potentially degrade constraints on the spectral index of the primordial power spectrum and its running by more than an order of magnitude. Our results also depend strongly on the maximum wavenumber of the power spectrum which can be used due to non-linearities.
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