Investigating a Possible Variation of the Gravitational Constant Through Gas Mass Fraction Measurements and Type Ia Supernovae Observations

Abstract

In this paper, we investigate a possible time variation of the gravitational constant (G) using a non-parametric approach. Our main cosmological probe is the gas mass fraction of galaxy clusters measured from X-ray observations. We also account for the effect of a varying $G$ on the intrinsic luminosity of type Ia supernovae (SNe Ia) through the Chandrasekhar mass-luminosity relation. We consider a specific phenomenological scenario, motivated by some scalar-tensor and screened modified-gravity frameworks, in which the standardized luminosity of SNe Ia decreases with increasing Chandrasekhar mass. Using gas mass fraction measurements jointly with luminosity distances from the Pantheon+ compilation, we reconstruct the evolution of G through Gaussian Processes. Our results indicate that a constant gravitational coupling remains broadly consistent with the data, although mild low-redshift departures are allowed.