  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 $\lbrace\Omega_m;w_0\rbrace
= \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.
