The minimally extended Varying Speed of Light (meVSL)
  Even though there have been the various varying speed of light (VSL)
cosmology models, they remain out of the mainstream because of their possible
violation of physics laws built into fundamental physics. In order to be the
VSL as a viable theory, it should inherit the success of special relativity
including Maxwell equations and thermodynamics at least. Thus, we adopt that
the speed of light, $\tilde c$ varies for the cosmic time not for the local
time, i.e., $\tilde c[z]$ where $z$ is the cosmological redshift. When one
describes the background FLRW universe, one can define the constant-time
hypersurface by using physical quantities such as temperature, density, and
$\tilde c$. It is because they evolve in time, and the homogeneity of the
Universe demands that they must equal at the equal cosmic time. The variation
of $\tilde c$ accompanies the joint variations of all related physical
constants in order to satisfy the Lorentz invariance, thermodynamics, and
Bianchi identity. We call this VSL model as a "minimally extended VSL (meVSL)".
We derive cosmological observables of meVSL and obtain the constraints on the
variation of $\tilde c$ by using the current observations. Interestingly, $z$
and all geometrical distances except the luminosity distance of meVSL are the
same as those of general relativity. However, the Hubble parameter of meVSL is
rescaled as $H = (1+z)^{-b/4} H^{(\rm GR)}$ which might be used as a solution
for the tension of the Hubble parameter measurements. In this manuscript, we
provide the main effects of meVSL on various cosmological observations
including BBN, CMB, SZE, BAO, SNe, GWs, H, SL, and $\Delta \alpha$.
