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We propose a new method for probing the time variation of the effectiveNewton's constant $G_{\rm eff}$, based on the optimal redshift weightingscheme, and demonstrate the efficacy using the DESI galaxy spectroscopicsurvey. We find that with the optimal redshift weights, the evolution of$G_{\rm eff}(z)$ can be significantly better measured: the uncertainty of$G_{\rm eff}(z)$ can be reduced by a factor of $2.2\sim12.8$ using the DESI BGSsample at $z \lesssim0.45$, and by a factor of $1.3\sim4.4$ using the DESI ELGsample covering $0.65\lesssim z\lesssim1.65$.

Probing the time variation of the effective Newton's constant with optimal redshift weights