A search for the variation of speed of light using galaxy clusters gas mass fraction measurements

In this paper, we implement a new model-independent method to test the invariance of the speed of light $c$ as a function of redshift, by combining the measurements of galaxy cluster gas mass fraction, $H(z)$ from cosmic chronometers, and type-Ia supernovae (SNe Ia). In our analyses, we consider both a constant depletion factor (which corresponds to the ratio by which $f_{gas}$ is depleted with respect to the universal baryonic mean) and one varying with redshift. We also consider the influence of different $H_0$ estimates on our results. We look for a variation of $c$, given by $c(z)=c_0(1+c_1z)$. It is found a degeneracy between our final results on $c$ variation and the assumptions on gas mass fraction depletion factor. Most of our analyses indicate negligible variation of the speed of light.