The semiclassical tunneling probability in quantum cosmologies with varying speed of light

TL;DR

This paper investigates how the tunneling probability for universe nucleation in quantum cosmology is affected by a varying speed of light, showing significant differences from constant c models especially at large cosmological constants.

Contribution

It introduces a new form of tunneling probability in VSL quantum cosmology, highlighting how it differs from traditional models with constant speed of light.

Findings

Tunneling probability in VSL cosmology is exponentially suppressed for large b3.

The probability depends on b3 and b1 in a different manner than in constant c models.

VSL models can address classical cosmological problems while altering nucleation probabilities.

Abstract

In quantum cosmology the closed universe can spontaneously nucleate out of the state with no classical space and time. The semiclassical tunneling nucleation probability can be estimated as $\emph{P}\sim\exp(-\alpha^2/\Lambda)$ where $\alpha$=const and $\Lambda$ is the cosmological constant. In classical cosmology with varying speed of light c(t) (VSL) it is possible to solve the horizon problem, the flatness problem and the $\Lambda$-problem if c=sa^n with s=const and n<-2. We show that in VSL quantum cosmology with n<-2 the semiclassical tunneling nucleation probability is $\emph{P}\sim\exp(-\beta^2\Lambda^k)$ with beta=const and k>0. Thus, the semiclassical tunneling nucleation probability in VSL quantum cosmology is very different from this one in quantum cosmology with c=const. In particular, this one is strongly suppressed for large values of $\Lambda$.