Charting the expansion of the Universe from z$\sim$0 to z$\sim$14 with HII galaxies
We present an updated Hubble diagram of giant extragalactic H II regions and H II galaxies spanning the redshift interval $z\sim 0$ to $z\sim 14$, extending the use of the $L(\mathrm{H}\beta)-\sigma$ relation as an independent cosmological probe into the epoch of cosmic dawn. Our sample comprises 243 objects, including local anchor systems with primary distance measurements, previously published low- and intermediate-redshift H II galaxies, recent JWST/NIRSpec observations, and a new subsample of extremely high-redshift H II galaxies observed with JWST and with ALMA+JWST for the highest-redshift cases. We homogenise the measurements across the full sample, applying consistent corrections for instrumental and thermal broadening, extinction, and, where required, the transformation from [O III]-based to Balmer-line velocity dispersions. We model lensing effects of high redshift using a log-normal magnification formalism and infer cosmological parameters via a nested-sampling analysis. The $L-\sigma$ relation remains consistent over the full redshift range, showing no evidence for significant evolution even at the highest redshifts currently accessible. For the joint anchor+H II galaxies sample, under a flat $\Lambda$CDM model, we obtain $h=0.725\pm0.040$ and $\Omega_m=0.308^{+0.043}_{-0.053}$. Allowing a constant dark-energy equation of state yields $w_0=-0.96^{+0.53}_{-0.21}$, while a CPL parametrisation gives $w_0=-0.92^{+0.57}_{-0.34}$ and $w_a=-0.48^{+0.60}_{-1.50}$, all consistent, within the uncertainties, with concordance cosmology. These results demonstrate that H II galaxies offer a viable, fully independent tracer of the expansion history across almost the entire age of the Universe, opening a new avenue for testing $\Lambda$CDM and dark-energy evolution well beyond reionisation.