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 catalogue of cosmic chronometers have tended to show that the speed of light appears to be constant, at least up to z ∼2. A notable exception is the use of high-redshift ultraviolet + X-ray quasars, whose Hubble diagram seems to indicate an ∼2.7σ deviation of c from its value c₀ (2.99792458 × 10¹⁰ 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 catalogue. When these deficiencies are addressed correctly, one finds that c/c₀ = 0.95 ± 0.14 in the redshift range 0 z 2, fully consistent with zero variation within the measurement errors.