Varying physical constants and the lithium problem
  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 $3 He/H=2.940(\pm 0.049){\times}10^{-5}$.
