A Galileon Design of Slow Expansion

We show a model of the slow expansion, in which the scale invariant spectrum of curvature perturbation is adiabatically induced by its increasing mode, by applying a generalized Galileon field. In this model, initially \epsilon << -1, which then is rapidly increasing, during this period the universe is slowly expanding. There is not the ghost instability, the perturbation theory is healthy. When \epsilon \sim -1, the slow expansion phase ends, and the available energy of field can be released and the universe reheats. This scenario might be a viable design of the early universe.