Geometrical tests of cosmological models

I. Probing dark energy using the kinematics of high redshift galaxies

¹ Centre de Physique Théorique (Centre de Physique Théorique is UMR 6207 – “Unité Mixte de Recherche” of CNRS and of the Universities “de Provence”, “de la Méditerranée” and “du Sud Toulon-Var” – Laboratory affiliated to FRUMAM (FR 2291).) , CNRS-Université de Provence, Case 907, 13288 Marseille, France e-mail: marinoni@cpt.univ-mrs.fr
² Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
³ Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02143, USA
⁴ Laboratoire d'Astrophysique de Marseille, UMR 6110, CNRS Université de Provence, 13376 Marseille, France

Received: 17 January 2007
Accepted: 2 August 2007

Abstract

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 , or to constrain the cosmic equation of state parameter for a smooth dark energy component (w = , -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 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 , can be uniquely diagnosed, and will minimally bias the confidence level contours in the [ , 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.