Varying constants quantum cosmology
Katarzyna Leszczyńska (Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland); Adam Balcerzak (Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, Copernicus Center for Interdisciplinary Studies, Sławkowska 17, 31-016 Kraków, Poland); Mariusz P. Da̧browski (Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, Copernicus Center for Interdisciplinary Studies, Sławkowska 17, 31-016 Kraków, Poland)
We discuss minisuperspace models within the framework of varying physical constants theories including Î-term. In particular, we consider the varying speed of light (VSL) theory and varying gravitational constant theory (VG) using the specific ansätze for the variability of constants: c(a) = c0 an and G(a)=G0 aq. 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 at 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.
