Inflationary field excursion in broad classes of scalar field models

In single field slow roll inflation models the height and slope of the potential are to satisfy certain conditions, to match with observations. This in turn translates into bounds on the number of e-foldings and the excursion of the scalar field during inflation. In this work we consider broad classes of inflationary models to study how much the field excursion starting from horizon exit to the end of inflation, $\Delta \phi $, can vary for the set of inflationary parameters given by Planck. We also derive an upper bound on the number of e-foldings between the horizon exit of a cosmologically interesting mode and the end of inflation. We comment on the possibility of having super-Planckian and sub-Planckian field excursions within the framework of single field slow roll inflation.
Comment: 10 pages, 4 figures, Matches with version published in PRD