Big Bang Nucleosynthesis Constraints on the CCC+TL Cosmology

We investigate whether Big Bang nucleosynthesis (BBN) remains compatible with the Covarying Coupling Constants plus Tired Light (CCC+TL) cosmology. In this framework, only quantities with explicit length dimensionality covary through a universal scaling function $f\left(z\right)$, while dimensionless constants and dimensionless ratios remain invariant. At the redshifts $z$ relevant to BBN, $f\left(z\right)$ approaches a constant plateau $f_{\text{max}}\left(z\right)\simeq 3$, and the tired-light contribution is negligible, so the early-time dynamics reduce to a global rescaling of dimensioned quantities. In particular, the Hubble expansion rate $H$ at fixed temperature $T$ satisfies $H_{\text{CTL}}\left(T\right)=f_{\text{max}}^{-1}{H}_{\mathrm{\Lambda }\text{CDM}}\left(T\right)$, implying a longer cooling time $\mathrm{\Delta }t$ between weak freeze-out and the onset of nucleosynthesis by the same factor (CCC+TL labeled as $\mathit{\text{CTL}}$). We find that BBN predictions are preserved provided the relevant interaction rates $\mathrm{\Gamma }$ and decay rates governing the neutron lifetime ${\tau }_n$ share the same plateau scaling as $H$, so that governing combinations such as $\mathrm{\Gamma }\text{/}H$ and $\text{exp}(-\mathrm{\Delta }t\text{/}{\tau }_n)$ remain invariant. Implementing these plateau rescalings in the Kawano/NUC123 network (via a single control parameter $\mathtt{\text{fctl}}\equiv f_{\text{max}}$) yields identical light-element abundances for $\mathtt{\text{fctl}}=1$ ($\mathrm{\Lambda }$CDM) and $\mathtt{\text{fctl}}=3\left(\text{CCC+TL}\right)$ to within ${10}^{-3}-{10}^{-4}$ level, consistent with numerical rounding. We also illustrate that adopting the lower late-time CCC+TL baryon density from the Pantheon+ data fit can reduce the ${}^7\text{Li}$ discrepancy but simultaneously increases D/H, implying that BBN alone does not select between the late-time baryon-density inferences considered here.