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 $n_s$ 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.

8 pages

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