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 $\approx 0.2\mathrm{mag}$ lower. Here, we propose that a rapid transition in the value of the relative effective gravitational constant ${\mu }_G\equiv \frac{G_{\mathrm{eff}}}{G_N}$ at $z_t\simeq 0.01$ could explain the lower luminosity (higher magnitude) of local supernovae, thus solving the $H_0$ crisis. In other words, here the tension is solved by featuring a transition at the perturbative rather than background level. 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 $\approx 0.2\mathrm{mag}$. 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 $\mathrm{Planck}/\mathrm{\Lambda }\mathrm{CDM}$ background expansion.

• Received 15 February 2021
• Accepted 29 June 2021

DOI:https://doi.org/10.1103/PhysRevD.104.L021303