Testing the CCC+TL cosmology with cosmic-chronometer measurements of the Hubble parameter

In a recent paper, it was shown that the Covarying Coupling Constants and Tired Light (CCC+TL) hybrid model yields the Hubble parameter $H(z)$ that is substantially different from its measured value using differential aging of quiescent galaxies as cosmic chronometers (CC). It was claimed that the fit of the CCC+TL model to the $H(z)$ data results in a best-fit value for the parameter $\alpha$, defining the strength of the co-variation of the constants, disagreeing with that for the SN~Ia data at the $\sim 6\sigma$ level. In this paper we re-examine the assumptions underlying such a comparison. Cosmic-chronometer measurements are designed to be independent of cosmological priors, but they nevertheless rely on stellar population synthesis models, isochrones, and age-dating calibrations developed within standard stellar-evolution physics. Therefore, even before introducing any specific correction factor, the present CC compilation cannot be regarded as a model-independent falsification of CCC+TL without recomputing the relevant stellar population models in that framework. In the absence of such a recalculation, we ask a more limited question: what type and magnitude of modification to the effective differential-age relation would be sufficient to remove the claimed tension? We show that a phenomenological factor of the form $\sim (1+z_t)^{-3}$ with $z_t$ being the TL contribution to the observed redshift, motivated by the scaling of gas cooling times for galaxy formation in the CCC+TL framework compared to $\Lambda\text{CDM}$, is sufficient to reduce the apparent discrepancy in $\alpha$ to $\sim 0.13\sigma$. Since $z_t = 0$ for the stellar model primarily developed from local stellar observations, the stellar-aging methods may be unable to verify $\sim (1+z_t)^{-3}$ dependence.