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

## TL;DR

This paper introduces a novel optimal redshift weighting method to improve measurements of the time variation of the effective Newton's constant, demonstrating significant uncertainty reduction with DESI survey data.

## Contribution

The paper presents a new optimal redshift weighting scheme for probing $G_{\rm eff}(z)$, enhancing measurement precision using DESI galaxy survey data.

## Key findings

- Uncertainty in $G_{\rm eff}(z)$ reduced by up to 12.8 times with DESI BGS data.
- Uncertainty in $G_{\rm eff}(z)$ reduced by up to 4.4 times with DESI ELG data.
- Method effectively improves constraints on the evolution of Newton's constant.

## Abstract

We propose a new method for probing the time variation of the effective Newton's constant $G_{\rm eff}$, 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 $G_{\rm eff}(z)$ 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 BGS sample at $z \lesssim0.45$, and by a factor of $1.3\sim4.4$ using the DESI ELG sample covering $0.65\lesssim z\lesssim1.65$.