Quantum cosmologies with varying speed of light and the $\Lambda$ problem

TL;DR

This paper explores quantum cosmologies with a varying speed of light, proposing models that solve the flatness, horizon, and cosmological constant problems without requiring inflation, and achieve high nucleation probability for the universe.

Contribution

It introduces quantum VSL cosmologies that address the $ ext{Lambda}$-problem and solve classical cosmological issues without inflation, which is a novel approach.

Findings

Quantum VSL cosmologies can have high nucleation probability ($P o 1$).

These models can naturally explain the observed $ ho_ ext{ extLambda}/ ho_c$ ratio.

They provide solutions to horizon and flatness problems without inflation.

Abstract

In quantum cosmology the closed universe can spontaneously nucleate out of the state with no classical space and time. For the universe filled with a vacuum of constant energy density 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, so once it nucleates, the universe immediately starts the de Sitter inflationary expansion. The probability $\emph{P} $ will be large for values of $\Lambda$ that are large enough, whereas $\Lambda$ of our Universe is definitely small. Of course, for the early universe filled with radiation or another ''matter'' the mentioned probability is large nevertheless ($\emph{P}\sim 1$) but in this case we have no inflation which is a standard solution for the flatness and horizon problems. In the other hand, the alternative solution of these problems can be obtained in framework of cosmologies with varying speed of light $c(t)$ (VSL). We show that, as a matter of principle, such quantum VSL cosmologies exist that $\emph{P}\sim 1$, $\rho_{_\Lambda}/\rho_c\sim 0.7$ ($\Lambda$-problem) and both horizon and flatness problems are solvable without inflation.