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We present independent determinations of cosmological parameters using thedistance estimator based on the established correlation between the Balmer lineluminosity, L(H$\beta$), and the velocity dispersion ($\sigma$) for HIIgalaxies (HIIG). These results are based on new VLT-KMOS high spectralresolution observations of 41 high-z ($1.3 \leq$ z $\leq 2.6$) HIIG combinedwith published data for 45 high-z and 107 z $\leq 0.15$ HIIG, while thecosmological analysis is based on the MultiNest MCMC procedure not consideringsystematic uncertainties. Using only HIIG to constrain the matter densityparameter ($\Omega_m$), we find $\Omega_m = 0.244^{+0.040}_{-0.049}$ (stat), animprovement over our best previous cosmological parameter constraints, asindicated by a 37% increase of the FoM. The marginalised best-fit parametervalues for the plane $\{\Omega_m; w_0\}$ = $\{0.249^{+0.11}_{-0.065};-1.18^{+0.45}_{-0.41}\}$ (stat) show an improvement of the cosmologicalparameters constraints by 40%. Combining the HIIG Hubble diagram, the cosmicmicrowave background (CMB) and the baryon acoustic oscillation (BAO) probesyields $\Omega_m=0.298 \pm 0.012$ and $w_0=-1.005 \pm 0.051$, which arecertainly compatible -- although less constraining -- than the solution basedon the joint analysis of SNIa/CMB/BAO. An attempt to constrain the evolution ofthe dark energy with time (CPL model), using a joint analysis of the HIIG, CMBand BAO measurements, shows a degenerate 1$\sigma$ contour of the parameters inthe $\{w_0,w_a\}$ plane.

Independent cosmological constraints from high-z HII galaxies: new results from VLT-KMOS data