International Journal of Modern Physics A · 1997 · 22 citations · 0 references
Natural SciencesPhysicsAstrophysicsGravitationRelativityCurved SpacetimeEinstein Field EquationsGeneral RelativityInflationary CosmologyConformal MappingInflationary PotentialInflaton Potential ReconstructionLegendre TransformationsScalar PerturbationsScalar Spectral IndexSlow-roll PerturbationsSpectral Index
Within Einstein's general relativity, a new method of reconstructing the inflaton potential U(ϕ) 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 COBE 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.