Inflationary cosmology with nonlinear dispersion relations
Abstract
We present a technique, {\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the dispersion relations generically become nonlinear. We construct explicitly the error bounds associated with the approximations and then study them in detail. With the understanding of the errors and the proper choice of the Liouville transformations of the differential equations of the perturbations, we show that the analytical solutions describe the exact evolution of the linear perturbations extremely well even only in the first-order approximations. As an application of the approximate analytical solutions, we calculate the power spectra and indices of scalar and tensor perturbations in the slow-roll inflation, and find that the amplitudes of the power spectra get modified due to the quantum effects, while the power spectrum indices remain the same as in the linear case.
Cite
@article{arxiv.1308.5708,
title = {Inflationary cosmology with nonlinear dispersion relations},
author = {Tao Zhu and Anzhong Wang and Gerald Cleaver and Klaus Kirsten and Qin Sheng},
journal= {arXiv preprint arXiv:1308.5708},
year = {2014}
}
Comments
The analysis of power spectra and indices of scalar and tensor perturbations are enlarged. Two figures added. arXiv admin note: text overlap with arXiv:1308.1104