It has recently been pointed out that a gravitational transition taking place at a recent redshift $z_t$, reducing the effective gravitational constant $G_{\mathrm{eff}}$ 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 $H(z{)}^2\sim G_{\mathrm{eff}}$, 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 [$\mathrm{\Delta }N(z_i)$]. 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 $G_{\mathrm{eff}}$ by $\mathrm{\Delta }{G}_{\mathrm{eff}}/G_{\mathrm{eff}}\simeq 0.6$ at $z_t\simeq 0.005$. Thus, in a conservative approach, this method can be used to impose constraints on a possible abrupt change of the gravitational constant taking place at very low redshifts.

• Received 23 January 2022
• Accepted 14 July 2022

DOI:https://doi.org/10.1103/PhysRevD.106.023526