Probing the Time Variation of the Effective Newton’s Constant with Optimal Redshift Weights

We propose a new method for probing the time variation of the effective Newton’s constant G eff, based on the optimal redshift weighting scheme, and demonstrate the efficacy using the DESI galaxy spectroscopic survey. We find that with the optimal redshift weights, the evolution of can be significantly better measured: the uncertainty of can be reduced by a factor of 2.2 ∼ 12.8 using the DESI Bright Galaxy Survey sample at z ≲ 0.45, and by a factor of 1.3 ∼ 4.4 using the DESI Emission Line Galaxies sample covering 0.65 ≲ z ≲ 1.65.