Towards a Precision Cosmology from Starburst Galaxies at z>2
  This work investigates the use of a well-known empirical correlation between the velocity dispersion, metallicity, and luminosity in H beta of nearby HII galaxies to measure the distances to HII-like starburst galaxies at high redshifts. This correlation is applied to a sample of 15 starburst galaxies with redshifts between z=2.17 and z=3.39 to constrain Omega_m, using data available from the literature. A best-fit value of Omega_m = 0.21 +0.30 -0.12 in a Lambda-dominated universe and of Omega_m = 0.11 +0.37 -0.19 in an open universe is obtained. A detailed analysis of systematic errors, their causes, and their effects on the values derived for the distance moduli and Omega_m is carried out. A discussion of how future work will improve constraints on Omega_m by reducing the errors is also presented. 
E.R. Siegel, R. Guzm\'an, Jorge P. Gallego, M. Ordu\~na L\'opez, P.   Rodr\'i guez Hidalgo