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Abstract

A possible resolution of the $^7$Li problem within the Standard Model Big-Bang Nucleosynthesis is presented. The key idea originates from the application of the Scale-Invariant Vacuum (SIV) paradigm to the BBN. However, here we arrive at the conclusion that Reparametrization Invariant Symmetry Scaling (RISS) is the more appropriate framework for the epoch of the BBN and use the SIV only as a guidance framework. The outcome is $\chi^2<0.04$ fit to the observed primordial abundances of $^4$He, D/H, $^3$He/D, and fit of $\chi^2\approx1$ when including $^7$Li/H observations. The results are obtained and compared to the known standard BBN values by utilizing the publicly available PRIMAT code. The resolution of the $^7$Li problem requires SIV-guided deviation from the local thermal equilibrium during BBN, such that the thermal energy of matter and radiation scale differently with respect to the SIV-conformal factor $\lambda$ during the BBN epoch. This may be viewed as conformal symmetry breaking due to cooling of plasma and the properties of matter. As such, the framework may be of relevance to the problem of the nuclear fusion as well. The deduced baryon matter content is $\Omega_b\approx12\%$ for unbroken SIV and $\Omega_b\approx38\%$ for partially broken SIV, but with $\lambda<1$ in both cases, which signals preference for Reparametrization Invariant Symmetry Scaling (RISS) over the conventional SIV viewpoint. Applying the RISS paradigm results in $\lambda>1$ and $\Omega_b\approx10\%$ with clear departure of $n_T$ away from the naive SIV suggested value. In all the cases where the $^7$Li problem is resolved, the baryon content is significantly higher than the usually accepted value of $\Omega_b\approx4.9\%$ within the $\Lambda$CDM. \keywords{Cosmology -- Primordial Nucleosynthesis -- dark matter, Reparametrization Invariance, Scale-Invariant Vacuum (SIV)}