Inflaton potential reconstruction without slow-roll

Abstract

We describe a method of obtaining the inflationary potential from observations which does not use the slow-roll approximation. Rather, the microwave anisotropy spectrum is obtained directly from a parametrized potential numerically, with no approximation beyond linear perturbation theory. This permits unbiased estimation of the parameters describing the potential, as well as providing the full error covariance matrix. We illustrate the typical uncertainties obtained using the Fisher information matrix technique, studying the $λϕ^4$ potential in detail as a concrete example.