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We report the first results of a programme aimed at studying the propertiesof high redshift galaxies with on-going massive and dominant episodes of starformation (HII galaxies). We use the $L(\mathrm{H}\beta) - \sigma$ distanceestimator based on the correlation between the ionized gas velocity dispersionsand Balmer emission line luminosities of HII galaxies and Giant HII regions totrace the expansion of the Universe up to $z \sim 2.33$. This approach providesan independent constraint on the equation of state of dark energy and itspossible evolution with look-back time.  Here we present high-dispersion (8,000 to 10,000 resolution) spectroscopy ofHII galaxies at redshifts between 0.6 and 2.33, obtained at the VLT usingXShooter. Using six of these HII galaxies we obtain broad constraints on theplane $\Omega_m - w_0$. The addition of 19 high-z HII galaxies from theliterature improves the constraints and highlights the need for high qualityemission line profiles, fluxes and reddening corrections. The 25 high-z HIIgalaxies plus our local compilation of 107 HII galaxies up to $z=0.16$ wereused to impose further constraints. Our results are consistent with recentstudies, although weaker due to the as yet small sample and low quality of theliterature data of high-z HII galaxies.  We show that much better and competitive constraints can be obtained using alarger sample of high redshift HII galaxies with high quality data that can beeasily obtained with present facilities like KMOS at the VLT.

On the road to precision cosmology with high redshift HII galaxies