Constraints on the minimally extended varying speed of light model using the Pantheon+ dataset

In the context of the minimally extended varying speed of light (meVSL) model, both the absolute magnitude and the luminosity distance of type Ia supernovae (SNe Ia) deviate from those predicted by general relativity (GR). Using data from the Pantheon$+$ survey, we assess the plausibility of various dark energy models within the framework of meVSL. Both the constant equation of state (EoS) of the dark energy model ($\omega$CDM) and the Chevallier-Polarski-Linder (CPL) parameterization model ($\omega = \omega_0 + \omega_a (1-a)$) indicate potential variations in the cosmic speed of light at the 1-$\sigma$ confidence level. For $\Omega_{\m0} = 0.30, 0.31$, and 0.32 with $(\omega_0 \,, \omega_a) = (-1 \,, 0)$, the 1-$\sigma$ range of $\dot{c}_0/c_0 \, (10^{-13} \, \text{yr}^{-1})$ is (-8.76 \,, -0.89), (-11.8 \,, 3.93), and (-14.8 \,, -6.98), respectively. Meanwhile, the 1-$\sigma$ range of $\dot{c}_0/c_0 (10^{-12} \, \text{yr}^{-1})$ for CPL dark energy models with $-1.05 \leq \omega_{0} \leq -0.95$ and $0.28 \leq \Omega_{\m0} \leq 0.32$, is (-6.31\,, -2.98). The value of $c$ at $z = 3$ can exceed that of the present by $0.2 \sim 3$ \% for $\omega$CDM models and $5 \sim 13$ \% for CPL models. Additionally, for viable models except for the CPL model with $\Omega_{\m0} = 0.28$, we find $-25.6 \leq \dot{G}_0/G_0 \, (10^{-12} \, \text{yr}^{-1}) \leq -0.36$. For this particular model, we obtain an increasing rate of the gravitational constant within the range $1.65 \leq \dot{G}_0/G_0 \, (10^{-12} \, \text{yr}^{-1}) \leq 3.79$. We obtained some models that do not require dark matter energy density through statistical interpretation. However, this is merely an effect of the degeneracy between model parameters and energy density and does not imply that dark matter is unnecessary.