Geometrical tests of cosmological models. I. Probing dark energy using the kinematics of high redshift galaxies

We suggest to use the observationally measured and theoretically justified correlation between size and rotational velocity of galactic discs as a viable method to select a set of high redshift standard rods which may be used to explore the dark energy content of the universe via the classical angular-diameter test. Here we explore a new strategy for an optimal implementation of this test. We propose to use the rotation speed of high redshift galaxies as a standard size indicator and show how high resolution multi-object spectroscopy and ACS/HST high quality spatial images, may be combined to measure the amplitude of the dark energy density parameter Ω_Q, or to constrain the cosmic equation of state parameter for a smooth dark energy component (w = p/ρ, -1 ≤ w < -1/3). Nearly 1300 standard rods with high velocity rotation in the bin V = 200 ± 20 km s^-1 are expected in a field of 1 sq. degree and over the redshift baseline 0 < z < 1.4. This sample is sufficient to constrain the cosmic equation of state parameter w at a level of 20% (without priors in the [Ω_m,Ω_Q] plane) even when the [OII]λ3727 Å linewidth-diameter relationship is calibrated with a scatter of ~40%. We evaluate how systematics may affect the proposed tests, and find that a linear standard rod evolution, causing galaxy dimensions to be up to 30% smaller at z = 1.5, can be uniquely diagnosed, and will minimally bias the confidence level contours in the [ Ω_Q, w] plane. Finally, we show how to derive, without a priori knowing the specific functional form of disc evolution, a cosmology-evolution diagram with which it is possible to establish a mapping between different cosmological models and the amount of galaxy disc/luminosity evolution expected at a given redshift.