A rapid transition of $G_{\rm eff}$ at $z_t \simeq 0.01$ as a solution
  of the Hubble and growth tensions
  The mismatch in the value of the Hubble constant from low- and high-redshift
observations may be recast as a discrepancy between the low- and high-redshift
determinations of the luminosity of Type Ia supernovae, the latter featuring an
absolute magnitude which is $\approx 0.2$~mag lower. Here, we propose that a
rapid transition in the value of the relative effective gravitational constant
$\mu_G\equiv\frac{G_{\rm eff}}{G_N}$ at $z_t\simeq 0.01$ could explain the
lower luminosity (higher magnitude) of local supernovae, thus solving the $H_0$
crisis. A model that features $\mu_G = 1$ for $z \lesssim 0.01$ but $\mu_G
\simeq 0.9$ for $z \gtrsim 0.01$ is trivially consistent with local
gravitational constraints but would raise the Chandrasekhar mass and so
decrease the absolute magnitude of Type Ia supernovae at $z \gtrsim 0.01$ by
the required value of $\approx 0.2$~mag. Such a rapid transition of the
effective gravitational constant would not only resolve the Hubble tension but
it would also help resolve the growth tension as it would reduce the growth of
density perturbations without affecting the Planck/$\Lambda$CDM background
expansion.
