Big Bang Nucleosynthesis Constraints on the CCC+TL Cosmology

Abstract

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 $H_{\text{CTL}} \left( T \right) = f^{-1}_{\text{max}} H_{\Lambda\text{CDM}}\left( T\right)$, implying a longer cooling time $\Delta t$ between weak freeze-out and the onset of nucleosynthesis by the same factor (CCC+TL labeled as $\textit{CTL}$). We find that BBN predictions are preserved provided the relevant interaction rates $\Gamma$ and decay rates governing the neutron lifetime ${\tau}_n$ share the same plateau scaling as $H$, so that governing combinations such as $\Gamma\text{/}H$ and $\text{exp} \left( -\Delta t \text{/} {\tau}_n \right)$ remain invariant. Implementing these plateau rescalings in the Kawano/NUC123 network (via a single control parameter $\texttt{fctl} \equiv f_{\text{max}}$) yields identical light-element abundances for $\texttt{fctl}= 1$ ($\Lambda$CDM) and $\texttt{fctl} = 3\left( \text{CCC+TL} \right)$ 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.