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 radio telescopes will detect in surveys of the sky in neutral hydrogen (H 1). We estimate the likely statistical errors if the standard ruler method were to be applied to such surveys. We emphasize uncertainties in our calculations, and pinpoint the most important features of future H I 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 (characterized 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 similar to 5 km, and given a reasonable survey duration (T-0 similar to 1 yr), we show that there will be negligible shot noise on a power spectrum derived from H I galaxies out to redshift z similar or equal to 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 greater than or similar to 10 deg(2) yr. A similar to 1-yr SKA survey would then contain greater than or similar to 10(9)(f(sky)/0.5) H I galaxies and provide constraints on the dark energy parameter w of order Delta w similar or equal to 0.01 (f(sky)/0.5)(-0.5), where f(sky) is the fraction of the whole sky observed.