Accurate extragalactic distance and dark energy: anchoring the distance scale with rotational parallaxes

We investigate how the current and future uncertainty on the Hubble constant affects the uncertainty in the equation of state (EOS) of dark energy (DE) (w) and the total density of the Universe (Omega(tot)). We start with the approximate linear relations between the cosmological parameters as presented by Spergel et al., and use the s.e. propagation relations to estimate the effects of improving the cosmic microwave background (CMB) parameters as well as the Hubble constant (H-0) on our knowledge of the EOS of DE. Because we do not assume a flat universe, we also estimate the attainable accuracy on Omega(tot) and the spatial curvature of the Universe. In one limiting case, we assume that the constraints provided by additional data (galaxy clustering, weak lensing and so forth) do not improve significantly, while the error on the Hubble constant is decreased by a factor of up to 10. The other limiting case of significantly improved additional data with current H-0 errors has been investigated by the Dark Energy Task Force (DETF). For the former scenario, we find that future improvements of the determination of the CMB hardly changes the accuracy with which the EOS and Omega(tot) are known, unless the Hubble constant can be measured with an accuracy of several per cent. The conclusion of the DETF is that the Hubble constant hardly matters if the additional data are sufficiently accurate. We find that a combination of moderate H-0 improvements with moderately improved 'other' data might significantly constrain the evolution of DE, but at a reduced cost. We review in some detail several methods that might yield extragalactic distances with errors of the order of several per cent, where we focus on the current and future strengths and weaknesses of the methods. Specifically we review the following: the velocity field method, two maser methods, four light echo techniques, two binary star methods and the 'rotational parallax' (RP) technique. Because these methods substantially rely on geometry rather than astrophysics or cosmology, their results are quite robust. In particular we focus on the advantages of the RP technique which can provide accurate (1 per cent), single-step and bias-free distances to Local Group galaxies. These distances can be used to improve the zero-point for other distance indicators which in turn would then be able to determine the Hubble constant to greater accuracy than they currently do. Achieving an accuracy of a few per cent in the zero-point distances to M 31, M 33 and the Large Magellanic Cloud by the RP method requires radial velocities at the 10 km s(-1) level and proper motions attainable by future astrometric missions such as SIM, GAIA and OBSS, or by future radio observatories such as the SKA.