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

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 ns and the running spectral index ns′ is obtained without using rapid roll or extended slow roll approximations. The cosmological consequences of the model is discussed.