Constraints on the time variation of the speed of light using Pantheon
  dataset
  Both the absolute magnitude of type Ia supernovae (SNe Ia) and the luminosity
distance of them are modified in the context of the minimally extended varying
speed of light (meVSL) model compared to those of general relativity (GR). We
have analyzed the likelihood of various dark energy models under meVSL by using
the Pantheon SNe Ia data. Both $\omega$CDM and CPL parameterization dark energy
models indicate a cosmic variation of the speed of light at the 1-$\sigma$
level. For $\Omega_{\text{m} 0} = 0.30, 0.31$, and 0.32 with $(\omega_0 \,,
\omega_a) = (-1 \,, 0)$, 1-$\sigma$ range of $\dot{\tilde{c}}_0/\tilde{c}_0 \,
(10^{-13} \, \text{yr}^{-1}) $ are (-8.76 \,, -0.89), (-11.8 \,, 3.93), and
(-14.8 \,, -6.98), respectively. Meanwhile, 1-$\sigma$ range of
$\dot{\tilde{c}}_0/\tilde{c}_0 (10^{-12} \, \text{yr}^{-1}) $ for the CPL dark
energy models with $-1.05 \leq \omega_{0} \leq -0.95$ and $0.28 \leq
\Omega_{\text{m} 0} \leq 0.32$, are (-6.31\,, -2.98). The value of $\tilde{c}$
at $z = 3$ can be larger than that of the present by $0.2 \sim 3$ \% for
$\omega$CDM models and $5 \sim 13$ \% for CPL models. We also obtain $-25.6
\leq \dot{\tilde{G}}_0/\tilde{G}_0 \, (10^{-12} \, \text{yr}^{-1}) \leq -0.36$
for viable models except for CPL model for $\Omega_{\text{m} 0} = 0.28$. We
obtain the increasing rate of the gravitational constant as $1.65 \leq
\dot{\tilde{G}}_0/\tilde{G}_0 \, (10^{-12} \, \text{yr}^{-1}) \leq 3.79$ for
that model.
