Challenges to a sharp change in $G$ as a solution to the Hubble tension

It has been proposed that the gravitational constant $G$ abruptly decreased around 130 Myr ago, making Type Ia supernovae (SNe) in the Hubble flow intrinsically brighter than 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 explore a wide range of unattractive consequences of this ``$G$ step model'' (GSM). We find that since the luminosities of Sun-like stars scale as approximately $G^{5.6}$, the Solar luminosity would have dropped substantially 130 Myr ago in this scenario, likely pushing Earth into a planetary glaciation. However, there was no Snowball Earth episode in the last 500 Myr. The 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 considerably alter stellar evolution, causing the Sun to have exhausted about 2/3 of its fuel supply rather than 1/2. This would make the Sun's helioseismic age exceed that of the oldest meteorite samples, but these agree excellently in practice. The expected age of the Universe also agrees well with that of the oldest Galactic stars assuming constant $G$. The GSM however implies these stars are younger, creating a lack of stars from the first 3 Gyr of cosmic history. These arguments pose significant challenges to models seeking to resolve the Hubble tension through a transition in $G$.