2016/04/30 by Tao Zhu, Anzhong Wang, Klaus Kirsten +2 · 29 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Gravitation #Gravitational potential #Gravitational redshift #Mathematics #Physics #Quantum #Quantum fluctuation #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Solar and Space Plasma Dynamics #Speed of gravity #Statistical physics #astro-ph.CO #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.93.123525
published in Physical review. D/Physical review. D. 93(12) (American Physical Society) · revtex4, 9 figures, no tables. Typos are corrected, and sections are rearranged. Version to appear in PRD
arxiv created 2016/06/21 · openalex publication_date 2016/06/29 · arxiv updated 2016/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we provide a systematic investigation of high-order primordial perturbations with nonlinear dispersion relations due to quantum gravitational effects in the framework of uniform asymptotic approximations. Because of these effects, the equation of motion of the mode function in general has multiple turning points. After obtaining analytically approximated solutions to any order in different regions, associated with different types of turning points, we match them to the third one. To this order the errors are less than 0.15%. General expressions of the power spectra of the primordial tensor and scalar perturbations are derived explicitly. We also investigate effects of backreactions of the quantum gravitational corrections, and make sure that inflation lasts long enough in order to solve the underlying problems, such as flatness, horizon, and monopole. Then we study various features of the spectra that are observationally relevant. In particular, under a moderate assumption about the energy scale of the underlying theory of quantum gravity, we have shown that the quantum gravitational effects may alter significantly the ratio between the tensor and scalar power spectra, thereby providing a natural mechanism to alleviate the tension between observations and certain inflationary models, including the one with a quadratic potential.