In this work, we analyze two possible alternative and model-independent
approaches to describe the inflationary period. The first one assumes a general
equation of state during inflation due to Mukhanov, while the second one is
based on the slow-roll hierarchy suggested by Hoffman and Turner. We find that,
remarkably, the two approaches are equivalent from the observational viewpoint,
as they single out the same areas in the parameter space, and agree with the
inflationary attractors where successful inflation occurs. Rephrased in terms
of the familiar picture of a slowly rolling, canonically normalized scalar
field, the resulting inflaton excursions in these two approaches are almost
identical. Furthermore, once the Galactic dust polarization data from Planck
are included in the numerical fits, inflaton excursions can safely take
sub-Planckian values.Comment: Revtex, 8 pages, 4 figures. References updated. Matches published
version in PR
