Charting the expansion of the Universe from z about 0 to z about 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 about 0 to z about 14, extending the use of the L(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 CDM model, we obtain h=0.725 plus or minus0.040 and 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 CDM and dark-energy evolution well beyond reionisation.