Independent cosmological constraints from high-z HII galaxies: new
  results from VLT-KMOS data
  We present independent determinations of cosmological parameters using the
distance estimator based on the established correlation between the Balmer line
luminosity, L(H$\beta$), and the velocity dispersion ($\sigma$) for HII
galaxies (HIIG). These results are based on new VLT-KMOS high spectral
resolution observations of 41 high-z ($1.3 \leq$ z $\leq 2.6$) HIIG combined
with published data for 45 high-z and 107 z $\leq 0.15$ HIIG, while the
cosmological analysis is based on the MultiNest MCMC procedure not considering
systematic uncertainties. Using only HIIG to constrain the matter density
parameter ($\Omega_m$), we find $\Omega_m = 0.244^{+0.040}_{-0.049}$ (stat), an
improvement over our best previous cosmological parameter constraints, as
indicated by a 37% increase of the FoM. The marginalised best-fit parameter
values 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 cosmological
parameters constraints by 40%. Combining the HIIG Hubble diagram, the cosmic
microwave background (CMB) and the baryon acoustic oscillation (BAO) probes
yields $\Omega_m=0.298 \pm 0.012$ and $w_0=-1.005 \pm 0.051$, which are
certainly compatible -- although less constraining -- than the solution based
on the joint analysis of SNIa/CMB/BAO. An attempt to constrain the evolution of
the dark energy with time (CPL model), using a joint analysis of the HIIG, CMB
and BAO measurements, shows a degenerate 1$\sigma$ contour of the parameters in
the $\{w_0,w_a\}$ plane.
