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

Abstract

We propose a new method for probing the time variation of the effective Newton's constant $G_{\mathrm{eff}}$, 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 $G_{\mathrm{eff}}(z)$ can be significantly better measured: the uncertainty of $G_{\mathrm{eff}}(z)$ can be reduced by a factor of $2.2\sim 12.8$ using the DESI BGS sample at $z\lesssim 0.45$, and by a factor of $1.3\sim 4.4$ using the DESI ELG sample covering $0.65\lesssim z\lesssim 1.65$.

8 pages, 4 figures; version to appear in ApJ

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