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

Nelson Videla

doi:10.1140/epjc/s10052-017-4711-2

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2017) 77: 142
https://doi.org/10.1140/epjc/s10052-017-4711-2

Regular Article - Theoretical Physics

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

Nelson Videla^*

Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile

^* e-mail: nelson.videla@ing.uchile.cl

Received: 12 December 2016
Accepted: 20 February 2017
Published online: 2 March 2017

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 $H(\phi )=H_{\mathrm{inf}}\exp [\frac{\frac{\phi }{m_\mathrm{p}}}{p\left( 1+\frac{\phi }{m_\mathrm{p}}\right) }]$ . 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.