Approximate consistency condition from a running spectral index in slow-roll inflationary models

2005/08/19 by Daniel J. H. Chung, Antonio Enea Romano
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Computer science #Consistency (knowledge bases) #Cosmology and Gravitation Theories #Geometry #Geophysics and Gravity Measurements #Index (typography) #Inflation (cosmology) #Length scale #Mathematics #Physics #Quantum mechanics #Scalar (mathematics) #Scale (ratio) #Solar and Space Plasma Dynamics #Spectral index #Spectral line #Statistical physics #Tensor (intrinsic definition) #Theoretical physics #Wavelength #astro-ph #hep-ph #hep-th

paper · pdf · doi:10.1103/physrevd.73.103510

published as Phys.Rev.D73:103510,2006 · 18 pages, 2 figures

arxiv created 2005/08/19 · openalex publication_date 2006/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Density perturbations generated from inflation almost always have a spectral index n_s which runs (varies with the wavelength). We explore a running spectral index scenario in which the scalar spectral index runs from blue (n_s>1) on large length scales to red (n_s<1) on short length scales. Specifically, we look for a correlation between the length scale at which n_s\ensuremath-1=0 and the length scale at which tensor to scalar ratio T/S reaches a minimum for single field slow-roll inflationary models. By computing the distribution of length scale ratios, we conclude that there indeed is a new approximate consistency condition that is characteristic of running spectral index scenarios that run from blue to red. Specifically, with strong running, we expect 96% of the slow-roll models to have the two length scales to be within a factor of 2, with the length scale at which the tensor to scalar ratio reaching a minimum longer than the wavelength at which n_s\ensuremath-1=0.

Citations

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