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 Omega(Q), or to constrain the cosmic equation of state parameter for a smooth dark energy component (omega = p/rho, - 1 = omega < -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 omega at a level of 20% (without priors in the [Omega(m),Omega(Q)] plane) even when the [OII]lambda 3727 angstrom linewidth-diameter relationship is calibrated with a scatter of similar to 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 [Omega(Q), omega] 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.