Tunneling decay rate in quantum cosmology

In canonical quantum cosmology, the wave function of the universe lacks explicit time dependence. However, time evolution may be present implicitly through the semiclassical superspace variables, which themselves depend on time in classical dynamics. In this paper, we apply this approach to an oscillating universe model recently introduced by Graham et al. By extending the model to include a massless, minimally coupled scalar field $\phi$ which has little effect on the dynamics but can play the role of a "clock", we determine the decay rate of the oscillating universe.