We present new high spectral resolution observations of 15 high-z ($1.3 leq$ z $leq 2.5$) HII Galaxies (HIIG) obtained with MOSFIRE at the Keck Observatory. These data, combined with already published data for another 31 high-z and 107 z $leq 0.15$ HIIG, are used to obtain new independent cosmological results using the distance estimator based on the established correlation between the Balmer emission line velocity dispersion and luminosity for HIIG. Our results are in excellent agreement with the latest cosmological concordance model ($Lambda$CDM) published results. From our analysis, we find a value for the mass density parameter of $Omega_m=0.290^{+0.056}_{-0.069}$ (stat). For a flat Universe we constrain the plane $lbraceOmega_m;w_0rbrace = lbrace 0.280^{+0.130}_{-0.100} ; -1.12^{+0.58}_{-0.32}rbrace $ (stat). The joint likelihood analysis of HIIG with other complementary cosmic probes (Cosmic Microwave Background and Baryon Acoustic Oscillations) provides tighter constraints for the parameter space of the Equation of State of Dark Energy that are also in excellent agreement with those of similar analyses using Type Ia Supernovae instead as the geometrical probe.
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