From inflationary core potentials to higher-order curvature scalar Lagrangians

Within Einstein's general relativity, a new method of reconstructing the inflaton potential U(phi) has been developed which, in principle, is applicable to any order of the slow-roll approximation. For the resulting second order nonlinear differential equation we found a new solution for which the spectral index of scalar perturbations is completely fixed as n(s) = 1.49575. This value fits quite well to recent COPE and other astrophysical observations. Via a Legendre transformation, we are able to reconstruct and visualize the corresponding nonlinear curvature scalar Lagrangian L(R) in which the inflaton is absorbed by means of a conformal mapping.