2005/07/31 by Kevork N. Abazajian, Kevork Abazajian, Kenji Kadota +1 · 1 citation
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Econometrics #Economics #Mathematical analysis #Mathematics #Physics #Power (physics) #Spectrum (functional analysis) #Taylor series #Thermodynamics #astro-ph #hep-ph
paper · pdf · doi:10.1088/1475-7516/2005/08/008
published as JCAP 0508:008,2005 · References added. Typo corrected
arxiv created 2005/08/23 · openalex publication_date 2005/08/23 · arxiv updated 2014/10/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The power spectrum is traditionally parametrized by a truncated Taylor series: . It is reasonable to truncate the Taylor series if , but it is not if . We argue that there is no good theoretical reason to prefer , and show that current observations are consistent with | n * 'ln( k / k * )| ∼ | n * − 1| even for |ln( k / k * )| ∼ 1. Thus, there are regions of parameter space, which are both theoretically and observationally relevant, for which the traditional truncated Taylor series parametrization is inconsistent, and hence it can lead to incorrect parameter estimations. Motivated by this, we propose a simple extension of the traditional parametrization, which uses no extra parameters, but that, unlike the traditional approach, covers well motivated inflationary spectra with | n * '| ∼ | n * − 1|. Our parametrization therefore covers not only standard slow-roll inflation models but also a much wider class of inflation models. We use this parametrization to perform a likelihood analysis for the cosmological parameters.