Varying constants quantum cosmology

TL;DR

This paper explores quantum cosmology models with varying physical constants, analyzing how changes in the speed of light and gravitational constant affect the universe's quantum tunneling probability from nothing, using WKB approximation.

Contribution

It introduces minisuperspace models with varying constants and applies WKB methods to evaluate tunneling probabilities, highlighting the impact of varying $c$ and $G$ on universe creation.

Findings

Tunneling potentials are mostly of the tunneling type, suitable for WKB analysis.

Probability of universe tunneling increases with growing $c$ and decreasing $G$.

Varying constants significantly alter tunneling probabilities compared to standard models.

Abstract

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.