Quantum Creation of a Universe in Albrecht-Magueijo-Barrow model

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 that in quantum cosmology with $c$=const. In particular, it can be strongly suppressed for large values of $\Lambda$. In addition, we propose the instanton which describes the nucleation of closed universes in VSL models. This solution is akin to the Hawking-Turok instanton in the means of O(4) invariance but, unlike to it, is non-singular. Moreover, using this solution we can obtain the probability of nucleation which is suppressed for large value of $\Lambda$ too.