Hints for a Gravitational Transition in Tully–Fisher Data

We use an up-to-date compilation of Tully–Fisher data to search for transitions in the evolution of the Tully–Fisher relation. Using an up-to-date data compilation, we find hints at $\approx 3\sigma$ level for a transition at critical distances $D_c\simeq 9$ Mpc and $D_c\simeq 17$ Mpc. We split the full sample in two subsamples, according to the measured galaxy distance with respect to splitting distance $D_c$, and identify the likelihood of the best-fit slope and intercept of one sample with respect to the best-fit corresponding values of the other sample. For $D_c\simeq 9$ Mpc and $D_c\simeq 17$ Mpc, we find a tension between the two subsamples at a level of $\Delta {\chi }^2>17\left(3.5\sigma \right)$. Using Monte Carlo simulations, we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances and is unlikely in the context of a homogeneous dataset constructed using the Tully–Fisher relation. If the tension is interpreted as being due to a gravitational strength transition, it would imply a shift in the effective gravitational constant to lower values for distances larger than $D_c$ by $\frac{\Delta G}{G}\simeq -0.1$. Such a shift is of the anticipated sign and magnitude but at a somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions ($\frac{\Delta G}{G}\simeq -0.1$ at the transition redshift of $z_t\lesssim 0.01$ ($D_c\lesssim 40$ Mpc)).