Varying constants quantum cosmology
  We discuss minisuperspace models within the framework of varying physical
constants theories including $\Lambda$-term. In particular, we consider the
varying speed of light (VSL) theory and varying gravitational constant theory
(VG) using the specific ans\"atze for the variability of constants: $c(a) = c_0
a^n$ and $G(a)=G_0 a^q$. We find that most of the varying $c$ and $G$
minisuperspace potentials are of the tunneling type which allows to use WKB
approximation of quantum mechanics. Using this method we show that the
probability of tunneling of the universe "from nothing" ($a=0)$ to a Friedmann
geometry with the scale factor $a_t$ is large for growing $c$ models and is
strongly suppressed for diminishing $c$ models. As for $G$ varying, the
probability of tunneling is large for $G$ diminishing, while it is small for
$G$ increasing. In general, both varying $c$ and $G$ change the probability of
tunneling in comparison to the standard matter content (cosmological term,
dust, radiation) universe models.
