Do current cosmological observations hint at the speed of light variability?
First author: Purba Mukherjee
The fundamental constants in Nature play a crucial role in the understanding of physical phenomena. Hence, it is of paramount importance to measure them with exquisite precision and to examine whether they present any variability across cosmic time, as a means to test the standard model of Cosmology, as well as fundamental physics. We revisit a consistency test of the speed of light variability proposed by Cai {\it et al.} using the latest cosmological observations, viz., Pantheon compilation of Type Ia Supernova luminosity distances (SN), cosmic chronometers from differential galaxy ages (CC), and measurements of both radial and transverse modes of baryonic acoustic oscillations ($r$-BAO and $a$-BAO) respectively. Such a test has the advantage of being independent of any assumption on the cosmic curvature - which can be degenerated with some variable speed of light models - as well as any dark energy model. We deploy the well-known Gaussian Processes to reconstruct cosmic distances and ages in the $0<z<2$ redshift range. Moreover, we examine the impact of cosmological priors on our analysis, such as the Hubble constant, supernova absolute magnitude, and the sound horizon scale. We find null evidence for the speed of light variability hypothesis for most choices of priors and data-set combinations, except for a mild deviation from it (at $\sim 2\sigma$ confidence level) at $z>1$ when the $a$-BAO data are included for some priors and reconstruction kernel cases. Still, we ascribe no statistical significance to this result for the incompleteness of this data set at such higher redshifts.