RECONSTRUCTING THE INFLATION POTENTIAL FOR AN ALMOST FLAT COBE SPECTRUM

Using the Hubble parameter as a 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 n(s) and the amplitudes of the scalar and the tenser spectrum. We find constraints between the values of n(s) and the corresponding values for the wavelength lambda. By imposing a dependence lambda(n(s)) we are 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 n(s).