An investigation of a varying G through Strong Lensing and SNe Ia observations

In this paper, we analyze the potential variation of the gravitational constant $G$ using data from strong gravitational lensing systems and Type Ia supernovae. Testing $G(z)$ parameterizations where $G(z)=G_0(1+G_{1}z)$ and $G(z)=G_0(1+z{)}^{G_1}$, we also account for the influence of $G$ on the luminosity of SNe Ia through the Chandrasekhar mass-luminosity relation. Only the flat universe hypothesis is considered. Constraints from 158 lensing systems and the Pantheon+ sample show no significant evidence of $G$ variation. However, although the results are compatible with no variation, the errors are not yet sufficiently restrictive to rule out any variation of $G$ with high statistical confidence. This study highlights the viability of using combined astrophysical data to probe variations in fundamental constants, suggesting that future surveys could refine these constraints.