A 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 in a rather simple way. The reconstruction is carried out in detail for two different types of Lagrangian, included in the frame of G-inflation, and explicit models for each Lagrangian are obtained. 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 impose the models to be stable. Thus, the method here developed provides a general and very efficient tool, a quite natural procedure in order to construct models consistent with very precise observations. It can be also applied to other models, besides the ones here considered.