Reconstructing the inflaton potential for an almost flat COBE spectrum.

Using the Hubble parameter as new ‘inverse time’ coordinate (H-formalism), a new method of reconstructing the inflaton potential is developed also using older results which, in principle, is applicable to any order of the slow-roll approximation. In first and second order, we need three observational data as inputs: the scalar spectral index ns and the amplitudes of the scalar and the tensor spectrum. We find constraints between the values of ns and the corresponding values for the wavelength λ. By imposing a dependence λ(ns), we were able to reconstruct and visualize inflationary potentials which are compatible with recent COBE and other astrophysical observations. From the reconstructed potentials, it becomes clear that one cannot find only one special value of the scalar spectral index ns. PACS no.: 98.80.Cq, 98.80.Hw, 04.20.-q, 04.20.Jb Typeset using REVTEX Electronic address: [email protected] [1.9.-19.12.95: c/o A. Maćias, [email protected]] Electronic address: [email protected] 1