A rapid transition of $G_{\rm eff}$ at $z_t \simeq 0.01$ as a solution of the Hubble and growth tensions

TL;DR

This paper proposes a rapid change in the effective gravitational constant at very low redshift to simultaneously address the Hubble constant discrepancy and the growth tension in cosmology.

Contribution

It introduces a model with a sudden transition in $G_{eff}$ at $z oughly 0.01$ that explains supernova luminosity differences and alleviates multiple cosmological tensions.

Findings

A transition in $G_{eff}$ can account for supernova luminosity discrepancies.

The model reduces growth of density perturbations without altering background expansion.

It is consistent with local gravitational constraints.

Abstract

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.