Stringent constraint on the CCC+TL cosmology with $H(z)$ Measurements

Recently, the Covarying Coupling Constants and Tired Light (CCC+TL) hybrid model was proposed to explain the unexpectedly small angular diameters of high-redshift galaxies observed by the James Webb Space Telescope (JWST) that are challenging to reconcile with the $\Lambda$CDM model. In this work, we test the CCC+TL model against model-independent Hubble parameter [$H(z)$] measurements obtained from cosmic chronometers. It turns out that the parameter set optimized for the type-Ia supernova (SN Ia) dataset within the CCC+TL model fails to reproduce the $H(z)$ data, but the $\Lambda$CDM model works well. Statistical comparison using the $\Delta\chi^2$ strongly favors $\Lambda$CDM over CCC+TL for the $H(z)$ data, with $\Delta \chi^2 = 61.52$. Crucially, the CCC+TL framework exhibits a severe internal tension, where the SN Ia-optimized speed-of-light variation index $\alpha$ is rejected by the $H(z)$ dataset with a likelihood ratio of $\it{R} \approx 1.7 \times 10^{-14}$. Our result suggests that the tension posed by JWST observations of compact high-$z$ galaxies may originate from the intrinsic properties and evolution of galaxies in the early universe.