Probing dark energy with baryonic oscillations and future radio surveys of neutral Hydrogen

Current surveys may be on the verge of measuring the baryonic oscillations in the galaxy power spectrum which are clearly seen imprinted on the Cosmic Microwave Background. It has recently been proposed that these oscillations allow a `standard ruler' method of probing the equation of state of dark energy. In this paper we present a new calculation of the number of galaxies future adio telescopes will detect in surveys of the sky in neutral Hydrogen (HI). We estimate the likely statistical errors if the standard ruler method were to be applied to such surveys. We emphasise uncertainties in our calculations, and pinpoint the most important features of future HI surveys if they are to provide new constraints on dark energy via baryonic oscillations. Designs of future radio telescopes are required to have a large bandwidth (characterised by \beta$, the ratio of the instantaneous bandwidth to the bandwidth required by survey) and to have the widest instantaneous (1.4 GHz) field of view ($FOV$) possible. Given the expected sensitivity of a future Square Kilometre Array (SKA), given that half of its collecting area will be concentrated in a core of diameter $\sim 5 ~ \rm km$, and given a reasonable survey duration ($T_0$ $\sim$ 1 yr), we show that there will be negligible shot noise on a power spectrum derived from HI galaxies out to redshift $z \simeq 1.5$. To access the largest cosmic volume possible by surveying all the sky available, we argue that $\beta$, $T_0$ and $FOV$ must obey the relation $\beta FOV T_0 \gtsimeq 10 \rm deg^2$ yr. An $\sim$1-yr SKA survey would then contain $\gtsimeq 10^{9} (f_{\rm sky}/0.5)$ HI galaxies and provide constraints on the dark-energy parameter $w$ of order $\Delta w \simeq 0.01 (f_{\rm sky}/0.5)^{-0.5}$