Logarithmic divergences in the κ-inflationary power spectra computed through the uniform approximation

Journal article


Alinea, Allan L., Kubota, Takahiro and Naylor, Wade. (2016). Logarithmic divergences in the κ-inflationary power spectra computed through the uniform approximation. Journal of Cosmology and Astroparticle Physics. 2016(2), pp. 1-31. https://doi.org/10.1088/1475-7516/2016/02/028
AuthorsAlinea, Allan L., Kubota, Takahiro and Naylor, Wade
Abstract

We investigate a calculation method for solving the Mukhanov-Sasaki equation in slow-roll k-inflation based on the uniform approximation (UA) in conjunction with an expansion scheme for slow-roll parameters with respect to the number of e-folds about the so-called turning point. Earlier works on this method have so far gained some promising results derived from the approximating expressions for the power spectra among others, up to second order with respect to the Hubble and sound flow parameters, when compared to other semi-analytical approaches (e.g., Green's function and WKB methods). However, a closer inspection is suggestive that there is a problem when higher-order parts of the power spectra are considered; residual logarithmic divergences may come out that can render the prediction physically inconsistent. Looking at this possibility, we map out up to what order with respect to the mentioned parameters several physical quantities can be calculated before hitting a logarithmically divergent result. It turns out that the power spectra are limited up to second order, the tensor-to-scalar ratio up to third order, and the spectral indices and running converge to all orders. This indicates that the expansion scheme is incompatible with the working equations derived from UA for the power spectra but compatible with that of the spectral indices. For those quantities that involve logarithmically divergent terms in the higher-order parts, existing results in the literature for the convergent lower-order parts calculated in the equivalent fashion should be viewed with some caution; they do not rest on solid mathematical ground.

Keywordsinflation; quantum field theory on curved space; cosmological pertubation theory; CMBR theory
Year2016
JournalJournal of Cosmology and Astroparticle Physics
Journal citation2016 (2), pp. 1-31
PublisherInstitute of Physics Publishing
ISSN1475-7516
Digital Object Identifier (DOI)https://doi.org/10.1088/1475-7516/2016/02/028
Scopus EID2-s2.0-84961140318
Research or scholarlyResearch
Page range1-31
Publisher's version
License
All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Online10 Feb 2016
Publication process dates
Accepted15 Jan 2016
Deposited10 Mar 2022
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