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

TL;DR

This paper explores a quasi-exponential inflationary model using the Hamilton-Jacobi approach, constraining its parameters with Planck 2015 data, and finds it consistent with current observational bounds.

Contribution

It introduces a novel quasi-exponential Hubble rate function in inflationary modeling and analyzes its viability using Planck data constraints.

Findings

Predicted tensor-to-scalar ratio r within Planck bounds

Model's scalar spectral index n_s matches observations

Running of spectral index dn_s/dlnk is consistent with data

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 $H(\phi)=H_{inf}\exp \left[\frac{\frac{\phi}{m_p}}{p\left(1+\frac{\phi}{m_p}\right)}\right]$. 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 $n_s-r$ 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 $dn_s/ d\ln k$ consistent with the current bounds imposed by Planck, and we conclude that the model is viable.