Cosmology with non-minimal scalar field: graceful entrance into   inflation
  We propose a scenario of the beginning of inflation in which the non-vacuum value of the scalar field that drives inflation develops dynamically due to the non-minimal coupling to gravity. In this scenario, inflation emerges as an intermediate stage of the evolution of the Universe, well after the Planck epoch, from a fairly general initial state. 
M.V. Libanov, V.A. Rubakov and P.G. Tinyakov