Varying physical constants and the lithium problem

Abstract: We have used the recently published varying physical constants (VPC) approach to resolve the primordial lithium abundance problem. The value of the ratio of $7Li$ to hydrogen $7Li/H=1.400(\pm 0.023){\times}10^{-10}$ we have calculated using this approach is about four times lower than that estimated using the standard lambda cold dark matter (${\Lambda}$CDM) cosmological model, and is consistent with the most agreed observational value of $1.6(\pm 0.3){\times}10^{-10}$. In the VPC approach Einstein equations are modified to include the variation of the speed of light $c$, gravitational constant $G$ and cosmological constant ${\Lambda}$ using the Einstein-Hilbert action. Application of this approach to cosmology naturally leads to the variation of the Plank constant $\hbar$ and the Boltzmann constant $k_B$ as well. They approach fixed values at the scale factor $a\ll 1$: $c=c_0/e$, $G=G_0/e^3$, $\hbar=\hbar_0/e$ and $k_B=k_{B0}/e^{5/4}$, where $e$ is the Euler's number (=2.7183). Since the VPC cosmology reduces to the same form as the ${\Lambda}$CDM cosmology at very small scale factors, we could use an existing Big-Bang nucleosynthesis (BBN) code AlterBBN with the above changes to calculate the light element abundances under the VPC cosmology. Among other abundances we have calculated at baryon to photon ratio ${\eta}=6.1{\times}10^{-10}$ are: $4He/H =0.2478 (\pm 0.041)$, $D/H =2.453(\pm 0.041){\times}10^{-5}$ and $3 He/H=2.940(\pm 0.049){\times}10^{-5}$.