2005/11/22 by H. P. de Oliveira, C. A. Terrero-Escalante, César A. Terrero–Escalante
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Applied mathematics #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Geometry #Geophysics and Gravity Measurements #Inflation (cosmology) #Inflaton #Inverse #Mathematics #Measure (data warehouse) #Physics #Robustness (evolution) #Statistical physics #Theoretical physics #astro-ph #hep-ph
paper · pdf · doi:10.1088/1475-7516/2006/01/024
published as JCAP 0601:024,2006
arxiv created 2005/11/22 · openalex publication_date 2006/01/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Robustness of the solutions to the inflaton potential inverse problem based on the slow-roll approximation is addressed. Here robustness is defined as the convergence of solutions to a unique functional form for the potential while increasing the order of the underlying expansion. For the analysis we introduce a measure of the difference of the outputs obtained using first and second order in the horizon-flow expansion. The evolution of this measure is determined by a second-order linear non-autonomous non-homogeneous differential equation. Boundedness of the general solutions to this equation is analysed. It is shown that they diverge for most of the physically meaningful cases. Examples for typical inflationary models are presented which confirm this result. The consequence is that the reconstructed inflationary potential depends in all its physical characteristics on the order of the approximation. It is argued that this lack of robustness is due to the limitations of the slow-roll expansion for probing the scale dependence of the inflationary spectra.