An analytic treatment of Quartic Hilltop Inflation

Abstract

Quartic hilltop inflation remains one of the most successful inflationary models. Yet, the expectations of early treatments of hilltop inflation would contradict the observations and render the model excluded. However, recent numerical treatment has demonstrated that quartic hilltop inflation actually fares well with observations. In this work, a fully analytic treatment of the model aims to dispel the mystery surrounding the behaviour of quartic hilltop inflation. The results obtained are in excellent agreement with numerical works on the subject, yet offer simple analytic formulas to calculate observables and easily test thereby quartic hilltop inflation, hopefully revealing information on the theoretical background.