2014/05/31 by Tao Zhu, Anzhong Wang, Gerald Cleaver +2 · 30 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gravitation #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Nonlinear system #Physics #Quantum #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Spectral density #Spectral line #Statistical physics #Statistics #astro-ph.CO #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.90.063503
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 90(6) (American Physical Society) · revtex, 5 tables. Added one figure, and various typos were corrected
openalex publication_date 2014/09/03 · arxiv created 2014/09/05 · arxiv updated 2014/09/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The uniform asymptotic approximation method provides a powerful, systematically improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the Friedmann-Robertson-Walker universe, designed especially for the cases where the relativistic linear dispersion relation is modified after gravitational quantum effects are taken into account. These include models from string/M Theory, loop quantum cosmology and Ho\ifmmode \checkr\else \vr\fiava-Lifshitz quantum gravity. In this paper, we extend our previous studies of the first-order approximations to high orders for the cases where the modified dispersion relation (linear or nonlinear) has only one turning point (or zero). We obtain the general expressions for the power spectra and spectral indices of both scalar and tensor perturbations up to the third order, at which the error bounds are \ensuremath\lesssim0.15%. As an application of these formulas, we calculate the power spectra and spectral indices in the slow-roll inflation with a nonlinear power-law dispersion relation. To check the consistency of our formulas, we further restrict ourselves to the relativistic case, and calculate the corresponding power spectra, spectral indices and runnings to the second order. Then, we compare our results with the ones obtained by the Green function method and show explicitly that the results obtained by these two different methods are consistent within the allowed errors.