The tunneling universe in scalar–tensor theory with matter: II

Abstract

In this paper, the wavefunction of the universe with a tunneling boundary condition is considered in the context of the Brans–Dicke-type theory with matter. In the (matter) case, the action is invariant under the field redefinition which is a sort of generalization of the scale factor duality. The universe undergoes quantum transition from a super-inflationary (pre-big bang) to a deflationary (post-big bang) phase. We calculate the transition rate from the wavefunction by solving the Wheeler–DeWitt equation and obtain a non-vanishing value. We learn that for a special value of the Brans–Dicke parameter the transition rate grows heavily. From the ten-dimensional string theory point of view this happens when three-dimensional branes (D3-brane) become dominant.