Hamilton\u2013Jacobi approach for quasi-exponential inflation: predictions and constraints after Planck 2015 results

Abstract

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(phi )=H_{mathrm{inf}}exp [frac{frac{phi }{m_mathrm{p}}}{pleft( 1+frac{phi }{m_mathrm{p}}right) }]. We analyze the inflation dynamics under the Hamilton–Jacobi approach, which allows us to consider H(phi ), rather than V(phi ), as the fundamental quantity to be specified. By comparing the theoretical predictions of the model together with the allowed contour plots in the n_mathrm{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 mathrm{d}n_mathrm{s}/ mathrm{d}ln k consistent with the current bounds imposed by Planck, and we conclude that the model is viable.