The cosmological lithium problem, varying constants and the $H_0$
  tension
  In this work we show that the cosmological lithium problem and the $H_0$
tension could be eased at the same time by allowing variations in the
fundamental constants. We compute the primordial abundances of light elements
resulting from Big Bang Nucleosynthesis considering the fine structure
constant, the Higgs' vacuum expectation value and Newton's constant as free
parameters. Using the observational data for abundances, we set constraints on
the variations of the fundamental constants. An interpretation of the results
in terms of the number of effective relativistic species gives $N_{\rm
eff}=4.04\pm0.12$. If one extrapolates the fit of {\sffamily Planck}
considering this $N_{\rm eff}$, the value of the inferred Hubble's constant
shifts to $H_0=(71.85\pm0.77)\,\text{km}\,\text{s}^{-1} \text{Mpc}^{-1}$,
compatible with current direct determinations.
