Phenomenological approaches of inflation and their equivalence

TL;DR

This paper compares two model-independent approaches to inflation, demonstrating their observational equivalence and showing that inflaton excursions can be sub-Planckian when including Planck data.

Contribution

It establishes the equivalence of the Mukhanov equation of state approach and the Hoffman-Turner slow-roll hierarchy in describing inflation.

Findings

Both approaches identify the same parameter space regions for successful inflation.

Inflaton excursions are nearly identical in both approaches.

Including Planck data allows for sub-Planckian inflaton excursions.

Abstract

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.