Title:Strong constraints on a sharp change in $G$ as a solution to the Hubble tension

Abstract:It has been proposed that if the gravitational constant $G$ abruptly decreased around 130 Myr ago, then Type Ia supernovae (SNe) in the Hubble flow would have a different luminosity to those in host galaxies with Cepheid distances. This would make Hubble flow SNe more distant, causing redshifts to rise slower with distance, potentially solving the Hubble tension. We find that since the luminosities of Sun-like stars scale as approximately $G^7$, the Solar luminosity would have dropped substantially 130 Myr ago in this scenario, pushing Earth into a planetary glaciation. However, there was no Snowball Earth episode in the last 500 Myr. The $G$ step model (GSM) also implies that the length of a year would have abruptly increased by about 10%, but the number of days per year has evolved broadly continuously according to geochronometry and cyclostratigraphy. The GSM would drastically alter stellar evolution, causing the Sun to have exhausted about 2/3 of its fuel supply rather than 1/2. This would lead to the helioseismic age of the Sun differing from that of the oldest meteorite samples, but these agree excellently in practice. There is also excellent agreement between the standard expansion history and that traced by cosmic chronometers, but these would disagree severely in the GSM. Moreover, distance indicators that use stellar luminosities would differ drastically beyond 40 Mpc from those that do not. These arguments cast very severe doubt on the viability of the GSM: the solution to the Hubble tension must be sought elsewhere.