Analyzing Pantheon SNeIa data in the context of Barrow's variable speed
  of light
  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 [1]. 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.
  [1] J.D. Barrow, Cosmologies with Varying Light-Speed, Phys. Rev. D 59,
043515 (1999); arXiv:astro-ph/9811022
