Quantum Creation of Closed Universe with Both Effects of Tunneling and Well

Abstract

A new ''twice loose shoe'' method in the Wheeler-DeWitt equation of the universe wave function on the cosmic scale factor a and a scalar field $ϕ$ is suggested in this letter. We analysis the both affects come from the tunneling effect of a and the potential well effect of $ϕ$, and obtain the initial values $a_0$ and $ϕ_0$ about a primary closed universe which is born with the largest probability in the quantum manner. Our result is able to overcome the ''large field difficulty'' of the universe quantum creation probability with only tunneling effect. This new born universe has to suffer a startup of inflation, and then comes into the usual slow rolling inflation. The universe with the largest probability maybe has a ''gentle'' inflation or an eternal chaotic inflation, this depends on a new parameter q which describes the tunneling character.