A general method for the construction of stable Galileon models
  consistent with the Planck data results
  The reconstruction procedure, which has proven quite useful to obtain viable
models of the universe evolution, is here employed in order to construct
inflation models. It has the advantages that it ensures full consistency with
astronomical observations and that it allows to evaluate the stability of the
resulting cosmological model quite easily. The reconstruction for two different
types of Lagrangian, included in the frame of G-inflation, is carried out in
detail and explicit models for each Lagrangian are constructed. As a bonus for
having used this reconstruction formalism, the final models are easily adjusted
to satisfy the observational constraints---imposed by the most recent data
releases of the Planck mission---on the spectral index, the tensor to scalar
ratio, and the running of the spectral index. Further, it turns also to be not
difficult to make the models stable. Thus, the method here developed provides a
general and very efficient tool, a quite natural procedure to construct models
consistent with very precise observations. It can also be applied to other
models, besides the ones here considered.
