This work investigates the use of a well-known empirical correlation between the velocity dispersion, metallicity and luminosity in Hβ of nearby H ii galaxies to measure the distances to H ii-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 Ωm, using data available from the literature. A best-fitting value of Ωm= 0.21+0.30−0.12 in a Λ-dominated universe and of Ωm= 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 Ωm is carried out. A discussion of how future work will improve constraints on Ωm by reducing the errors is also presented.
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Siegel et al. (2005) studied this question.
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