To determine whether or not H ii starburst galaxies (H iiG) are standardizable candles, we study the correlation between the $\mathrm{H}\beta$ luminosity ($L$) and the velocity dispersion ($\sigma$) of the ionized gas from H iiG measurements by simultaneously constraining the $L-\sigma$ relation parameters and the cosmological model parameters. We investigate six flat and nonflat relativistic dark energy cosmological models. We find that low-redshift and high-redshift H iiG data subsets are standardizable but obey different $L-\sigma$ relations. Current H iiG data are too sparse and too nonuniformly distributed in redshift to allow for a determination of why the samples follow different relations, but it could be caused by the high-redshift sample containing relatively fewer intrinsically dimmer sources (Malmquist bias) or it could be a consequence of H iiG evolution. Until this issue is better understood, H iiG data cosmological constraints must be treated with caution.

• Cosmological parameters
• Cosmology
• Dark energy