Testing $f(T)$ cosmologies with HII Hubble diagram and CMB distance priors

In this work, we present independent determinations of cosmological parameters and new constraints on $f(T)$ cosmologies, employing two new catalogs related to HII galaxy Hubble and CMB distance priors, along with the local standard measurements, SNIa, $H(z)$ measurements, growth rate data (RSD), and BAO baselines. We found that the marginalised best-fit C.L. H₀ and σ₈ parameters within these cosmologies can relax the current cosmological tensions using HIIG data. This produces a larger range of admissible values for the current Hubble constant, and when all baselines are considered, the uncertainty bands for H₀ and the matter density parameter reduce significantly.