Hamilton–Jacobi approach for quasi-exponential inflation: predictions and constraints after Planck 2015 results

In the present work we study the consequences of considering an inflationary universe model in which the Hubble rate has a quasi-exponential dependence in the inflaton field, given by H(ϕ)=Hinfexp[ϕmpp(1+ϕmp)]. We analyze the inflation dynamics under the Hamilton–Jacobi approach, which allows us to consider H(ϕ) , rather than V(ϕ) , as the fundamental quantity to be specified. By comparing the theoretical predictions of the model together with the allowed contour plots in the n_s- r plane and the amplitude of primordial scalar perturbations from the latest Planck data, the parameters charactering this model are constrained. The model predicts values for the tensor-to-scalar ratio r and for the running of the scalar spectral index d n_s/ d ln k consistent with the current bounds imposed by Planck, and we conclude that the model is viable.