Model-independent confirmation of a constant speed of light over cosmological distances

Recent attempts at measuring the variation of $c$ using an assortment of standard candles and the redshift-dependent Hubble expansion rate inferred from the currently available catalog of cosmic chronometers have tended to show that the speed of light appears to be constant, at least up to $z\sim 2$. A notable exception is the use of high-redshift UV $+$ X-ray quasars, whose Hubble diagram seems to indicate a $\sim 2.7\sigma$ deviation of c from its value $c_0$ ($\equiv 2.99792458\times {10}^{10}$ cm s${}^{-1}$) on Earth. We show in this paper, however, that this anomaly is due to an error in the derived relation between the luminosity distance, $D_L$, and $H(z)$ when $c$ is allowed to vary with redshift, and an imprecise calibration of the quasar catalog. When these deficiences are addressed correctly, one finds that $c\mathrm{/}{c}_0=0.95\pm 0.14$ in the redshift range $0\lesssim z\lesssim 2$, fully consistent with zero variation within the measurement errors.