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The tunneling universe in scalar–tensor theory with matter

In this paper, the wavefunction of the universe with a tunneling boundary condition is considered in the context of the Brans–Dicke-type scalar–tensor theory with matter. The matter may be interpreted as a D-particle (or -brane) in string theory when the Brans–Dicke parameter ω is . We study two simple examples. The first example, the (matter) case, has a scale factor duality even if the low energy string action is coupled to matter. The universe undergoes quantum transition from super-inflationary (pre-big-bang) to deflationary (post-big-bang) phase. We calculate the transition rate by solving the Wheeler–DeWitt equation and find that it is non-vanishing. The two phases are disconnected classically. The second example is the (radiation) case. With the help of earlier work this matter can be identified with a -brane in string theory. In this case, due to the absence of the scale factor duality and the complicated relations between scale factor and dilaton, it is hard to interpret the wavefunction as a pre- and post-big-bang phase.