The Hubble Flow of Plateau Inflation

TL;DR

This paper introduces a new method for analyzing the Hubble flow during inflation, comparing Taylor and Padé parametrizations, with implications for inflationary models and data interpretation.

Contribution

It develops an analytic solution approach for flow equations using different parametrizations, enhancing inflationary model analysis and potential reconstruction.

Findings

Padé approximants better capture plateau inflation features

New method improves convergence and reduces prior dependence

Results inform inflationary potential reconstruction

Abstract

In the absence of CMB precision measurements, a Taylor expansion has often been invoked to parametrize the Hubble flow function during inflation. The standard "horizon flow" procedure implicitly relies on this assumption. However, the recent Planck results indicate a strong preference for plateau inflation, which suggests the use of Pad\'e approximants instead. We propose a novel method that provides analytic solutions of the flow equations for a given parametrization of the Hubble function. This method is illustrated in the Taylor and Pad\'e cases, for low order expansions. We then present the results of a full numerical treatment scanning larger order expansions, and compare these parametrizations in terms of convergence, prior dependence, predictivity and compatibility with the data. Finally, we highlight the implications for potential reconstruction methods.