2001/09/30 by Steen H. Hansen, S. H. Hansen, M. Kunz +1 · 24 citations
Physics and Astronomy · #Astrophysics and Star Formation Studies #Bounded function #Constraint (computer-aided design) #Derivative (finance) #Flow (mathematics) #High-Energy Particle Collisions Research #Inflaton #Solar and Space Plasma Dynamics #Space (punctuation) #astro-ph #hep-ph
paper · pdf · doi:10.1046/j.1365-8711.2002.05855.x
published in Monthly Notices of the Royal Astronomical Society 336(3), 1007-1010 (Oxford University Press) · 4 pages, 2 figures. Important sign mistake corrected. Conclusions, abstract and discussion changed
arxiv created 2002/06/28 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Direct observations provide constraints on the first two derivatives of the inflaton potential in slow-roll models. We discuss how present-day observations, combined with the flow equations in slow-roll parameter space, provide a non-trivial constraint on the third derivative of the inflaton potential. We find a lower bound on the third derivative of the inflaton potential V″′/V > −0.2. We also show that unless the third derivative of the inflaton potential is unreasonably large, then one predicts the tensor-to-scalar ratio, r, to be bounded from below r > 3 × 10−6.