Quantum cosmology with matter in scalar–tensor theory

Abstract

The cosmological application of the low energy effective action of string theory with perfect fluid type matter (satisfying $p=\gamma \rho$) is reconsidered. First, its isotropic and anisotropic spacetime cosmological solutions are obtained for general $\gamma$. The scale factor duality is applied and checked for our model as well as in the presence of $\gamma$ of which possible extension to nonvanishing $\gamma$ is pioneered before. The asymptotic behavior of the solutions is investigated because of the complexity of the solutions. Second, as a quantization, we apply the canonical quantization and the corresponding Wheeler–De Witt equation is constructed for this scalar–tensor theory. By solving the Wheeler–De Witt equation the wave function is found for general value of $\gamma$. On the basis of its wave function, the tunneling rate turns out to be just the ratio of norms of the wave function for pre- and post-big-bang phases. This result shows that the rate grows as $\gamma$ gets value close to a specific value. This resolves the undetermined value for the behavior of the scale factors.