Towards an analytic solution of rapid roll inflation with a quartic potential

TL;DR

This paper derives an analytic solution for rapid roll inflation with a quartic potential, using Jacobi elliptic functions, and calculates spectral indices without common approximations, discussing cosmological implications.

Contribution

It provides a novel analytic solution to the inflaton dynamics in rapid roll inflation with a quartic potential, avoiding typical slow roll assumptions.

Findings

Analytic solution using Jacobi elliptic functions

Spectral index and running calculated without slow roll approximations

Discussion of cosmological consequences of the model

Abstract

In this paper, I present an analytic solution to the equation of motion of the inflaton field in a model of rapid roll inflation with a quartic potential by assuming that the Hubble parameter is a constant during inflation. The result is obtained by using Jacobi elliptic functions. The spectral index $n_s$ and the running spectral index $n_s^\prime$ is obtained without using rapid roll or extended slow roll approximations. The cosmological consequences of the model is discussed.