Examining the validity of the minimal varying speed of light model through cosmological observations: relaxing the null curvature constraint

Abstract

We revisit a consistency test for the speed of light variability, using the latest cosmological observations. This exercise can serve as a new diagnostics for the standard cosmological model and distinguish between the minimal varying speed of light in the Friedmann-Lemaître-Robertson-Walker universe. We deploy Gaussian processes to reconstruct cosmic distances and ages in the redshift range $0<z<2$ utilizing the 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 baryon acoustic oscillations ($r$-BAO and $a$-BAO) respectively. Such a test has the advantage of being independent of any non-zero cosmic curvature assumption - which can be degenerated with some variable speed of light models - as well as any dark energy model. We also 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. However, mild deviations are seen at $\sim 2σ$ confidence level for redshifts $z<1$ with some specific prior choices when $r$-BAO data is employed, and at $z>1$ with a particular reconstruction kernel when $a$-BAO data are included. Still, we ascribe no statistical significance to this result bearing in mind the degeneracy between the associated priors for combined analysis, and incompleteness of the $a$-BAO data set at higher $z$.