Mapping the Hubble Flow from z$ \sim $0 to z$ \sim$7.5 with HII Galaxies

Over twenty years ago, Type Ia Supernovae (SNIa) observations revealed an accelerating Universe expansion, suggesting a significant dark energy presence, often modelled as a cosmological constant, $\Lambda$. Despite its pivotal role in cosmology, the standard $\Lambda$CDM model remains largely underexplored in the redshift range between distant SNIa and the Cosmic Microwave Background (CMB). This study harnesses the James Webb Space Telescope's advanced capabilities to extend the Hubble flow mapping across an unprecedented redshift range, from $z \approx 0$ to $z \approx 7.5$. Using a dataset of 231 HII galaxies and extragalactic HII regions, we employ the $\text{L}-\sigma$ relation that correlates the luminosity of Balmer lines with their velocity dispersion, to define a competitive technique for measuring cosmic distances. This approach allows the mapping of the Universe expansion history over more than 12 billion years, covering 95\% of its age. Our analysis, using Bayesian inference, constrains the parameter space $\lbrace h, \Omega_m, w_0\rbrace = \lbrace 0.731\pm0.039, 0.302^{+0.12}_{-0.069}, -1.01^{+0.52}_{-0.29}\rbrace$ (statistical) for a flat Universe. Our results provide new insights into cosmic evolution and imply a lack of change in the photo-kinematical properties of the young massive ionizing clusters in HII galaxies across most of the history of the Universe.