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In the present work we study the consequences of considering an inflationaryuniverse model in which the Hubble rate has a quasi-exponential dependence inthe inflaton field, given by $H(\phi)=H_{inf}\exp\left[\frac{\frac{\phi}{m_p}}{p\left(1+\frac{\phi}{m_p}\right)}\right]$. Weanalyze the inflation dynamics under the Hamilton-Jacobi approach, which allowsus to consider $H(\phi)$, rather than $V(\phi)$, as the fundamental quantity tobe specified. By comparing the theoretical predictions of the model togetherwith the allowed contour plots in the $n_s-r$ plane and the amplitude ofprimordial scalar perturbations from the latest Planck data, the parameterscharactering this model are constrained. The model predicts values for thetensor-to-scalar ratio $r$ and for the running of the scalar spectral index$dn_s/ d\ln k$ consistent with the current bounds imposed by Planck, and weconclude that the model is viable.

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