1994/03/19 by Edward W. Kolb, Sharon L. Vadas
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Eternal inflation #Geometry #Inflation (cosmology) #Inflaton #Mathematical physics #Mathematics #Physics #Planck #Quantum mechanics #Scalar (mathematics) #Slow roll #Solar and Space Plasma Dynamics #Spectral index #Spectral line #Tensor (intrinsic definition) #astro-ph #gr-qc #hep-ph
paper · pdf · doi:10.1103/physrevd.50.2479
published as Phys.Rev. D50 (1994) 2479-2487 · 18 pages, LaTeX, no figures, FNAL--PUB--94/046-A; CfPA 94-th-14 (small revisions only, esp. examples for hybrid inflation)
arxiv created 1994/03/19 · openalex publication_date 1994/08/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Within an expansion in slow-roll inflation parameters, we derive the complete second-order expressions relating the ratio of tensor to scalar density perturbations and the spectral index of the scalar spectrum. We find that ``corrections'' to previously derived formulas can dominate if the tensor to scalar ratio is small. For instance, if VV''/(V')2\ensuremath≠1 or if [mPl2/(4\ensuremathπ)]\ensuremath\VertV'''/V'\ensuremath\Vert\ensuremath\gtrsim1, where V(\ensuremathφ) is the inflaton potential and mPl is the Planck mass, then the previously used simple relations between the indices and the tensor to scalar ratio fails. This failure occurs in particular for natural inflation, Coleman-Weinberg inflation, and ``chaotic'' inflation.