A model-independent test of speed of light variability with cosmological observations

Abstract: A powerful test of fundamental physics consists on probing the variability of fundamental constants in Nature. Although they have been measured on Earth laboratories and in our Solar neighbourhood with extremely high precision, it is crucial to carry out these tests at the distant Universe, as any significant variation of these quantities would immediately hint at new physics. We perform a cosmological measurement of the speed of light using the latest Type Ia Supernova and cosmic chronometer observations at the redshift range $0<z<2$. Our method relies on the numerical reconstruction of these data in order to circumvent {\it a priori} assumptions of the underlying cosmology. We confirm the constancy of the speed of light at such redshift range, reporting two $\sim 5$\% precision measurements of $c = (3.20 \pm 0.16) \; \times 10^5 \; \mathrm{km \; s}^{-1}$ in $z \simeq 1.58$, and $c = (2.67 \pm 0.14) \; \times 10^5 \; \mathrm{km \; s}^{-1}$ in $z \simeq 1.36$, depending on the reconstruction method, at a $1\sigma$ confidence level.