A&A 478, 43-55 (2008)

DOI: 10.1051/0004-6361:20077116

## Geometrical tests of cosmological models

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

**C. Marinoni**

^{1}, A. Saintonge^{2}, R. Giovanelli^{2}, M. P. Haynes^{2}, K. L. Masters^{3}, O. Le Fèvre^{4}, A. Mazure^{4}, P. Taxil^{1}, and J.-M. Virey^{1}^{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]3727 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
[, *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.

**Key words:**cosmology: observations

**--**cosmology: theory

**--**cosmology: cosmological parameters

**--**galaxies: high-redshift

**--**galaxies: fundamental parameters

**--**galaxies: evolution

**©**

*ESO 2008*