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 $3 He/H=2.940(\pm 0.049){\times}10^{-5}$.