2ND-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 no nlinear second order slow-roll approximation, we found, besides the po wer law inflation for n(s) < 1, an exact solution for which the spectr al index is necessarily determined as n(s) similar or equal to 1.5. Pa rt of these continuous and discrete spectra of the index fits within t he 1 sigma 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 n(s) which is related to effective string models.