2005/06/30 by A. Makarov, Alexey Makarov · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Geophysics and Gravity Measurements #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.72.083517
published as Phys.Rev. D72 (2005) 083517 · Matches the published PRD version; added comments on Abazaijan, Kadota and Stewart (2005) parameterization
arxiv created 2005/10/19 · openalex publication_date 2005/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the accuracy of slow-roll inflation in light of current observational constraints, which do not allow for a large deviation from scale invariance. We investigate the applicability of the first and second order slow-roll approximations for inflationary models, including those with large running of the scalar spectral index. We compare the full numerical solutions with those given by the first and second order slow-roll formulas. We find that even first order slow roll is generally accurate; the largest deviations arise in models with large running where the error in the power spectrum can be at the level of 1%--2%. Most of this error comes from inaccuracy in the calculation of the slope and not of the running or higher order terms. Second order slow roll does not improve the accuracy over first order. We also argue that in the basis ϵ0=1/H, ϵn+1=dln|ϵn|/dN, introduced by Schwarz et al. (2001), slow roll does not require all of the parameters to be small. For example, even a divergent ϵ3 leads to finite solutions which are accurately described by a slow-roll approximation. Finally, we argue that power spectrum parametrization recently introduced by Abazaijan, Kadota and Stewart does not work for models where spectral index changes from red to blue, while the usual Taylor expansion remains a good approximation.