Constraining a late time transition of $G_{\rm eff}$ using low-z galaxy
  survey data
  It has recently been pointed out that a gravitational transition taking place
at a recent redshift $z_t$, reducing the effective gravitational constant
$G_{\rm eff}$ by about $10\%$ for $z>z_t$, has the potential to lead to a
resolution of the Hubble tension if $z_t\lesssim 0.01$. Since $H(z)^2\sim
G_{\rm eff}$, such a transition would also lead to sharp change of the slope of
the Hubble diagram at $z=z_t$ and a sharp decrease in the number of galaxies
per redshift bin at $z_t$. Here we attempt to impose constraints on such a
transition by using two robust low-z redshift survey datasets ($z<0.01$), taken
from the Six-degree Field Galaxy Survey (6dFGS) as well as the 2MASS Redshift
Survey (2MRS). In both surveys, we bin the data in redshift bins and focus on
the number of galaxies in each bin ($\Delta N(z_i)$). We observe a peak in the
distribution of galaxies near a distance of approximately 20 Mpc in both
datasets. This feature could be attributed to galactic density fluctuations, to
coherent peculiar velocities of galaxies or to an ultra late-time gravitational
transition in the same era. In the context of the later scenario we show that
this feature could have been induced by a sharp change of $G_{\rm eff}$ by
$\Delta G_{\rm eff}/G_{\rm eff} \simeq 0.6$ at $z_t\simeq 0.005$. In a
conservative approach we can then impose a bound on such gravitational
transition as $\Delta G_{\rm eff}/G_{\rm eff} \lesssim 0.6$. We conclude that
the required level of gravitational transition $\Delta G/G \simeq 0.1$ for the
resolution of the Hubble tension can not be excluded by redshift survey data at
$z<0.01$.
