Analyzing Pantheon SNeIa data in the context of Barrow's variable speed of light

Abstract: We analyze the Combined Pantheon Sample of Type Ia supernovae while allowing the velocity of light to vary as a function of the scale factor $c\propto a^{-\zeta}$, as initiated by Barrow [Phys. Rev. D 59, 043515 (1999)]. The variation in the velocity of light creates an effect akin to the refraction phenomenon which occurs for a wave traveling in a medium with varying speed of wave. We elucidate the role of the local scale of gravitationally-bound regions in assisting the refraction effect to manifest. The refraction effect alters the redshift formulae (Lemaitre, distance-vs-z, luminosity distance-vs-z) and warrants a new analysis of the Pantheon dataset. Upon a reformulation of the distance-redshift relations, we achieve a high-quality fit of the Pantheon dataset to the variable light speed approach; the fit is as robust as that obtained in the standard $\Lambda CDM$ model. We find that the Pantheon dataset is consistent with the variable light speed of the functional form: $a\propto t^{\mu}$ and $c\propto a^{1-1/\mu}$ with (i) the cosmic age $t_{0}\approx 13.9$ Gy as a free parameter, while $\mu$ is unspecified; and (ii) a monotonic variation in the local scale for gravitationally-bound objects (applicable to the emission sources and the Solar System-based apparatus/observer). Due to the agent in (ii), the high-z portion of the Pantheon dataset would produce an "effective" $H_{0}$ estimate which is 10 percent lower than the $H_{0}$ estimate obtained from the low-z portion of the dataset. We offer an alternative interpretation of the accelerating expansion by way of variable speed of light, and as a by-product of the agent uncovered in (ii), a tentative suggestion toward "resolving" the ongoing tension in the Hubble constant estimates.