Second-order reconstruction of inflationary dynamics compatible with recent COBE data

A new method is applied to reconstruct the inflationary potential from a more phenomenological point of view. By using the more stringent nonlinear second order slow-roll approximation, we found, besides the power law inflation for ns < 1, an exact solution for which the spectral index is necessarily determined as ns ⋍ 1.5. Part of these continuous and discrete spectra of the index fits within the 1σ range of recent COBE and CAT data. In the conformal frame, the inflation can be absorbed in a specific nonlinear curvature scalar Lagrangian parametrized by ns which is related to effective string models.