http://arxiv.org/abs/1604.05739
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 {\em 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 in different regions, associated with different types of turning points, to any order, 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 back-reactions of the quantum gravitational corrections, and make sure that inflation lasts long enough in order to solve underlying problems, such as flatness, horizon and monopole. Various features of the spectra that are observationally relevant are investigated. 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.
T. Zhu, A. Wang, K. Kirsten, et. al.
Thu, 21 Apr 16
44/61
Comments: revtex4, 8 figures, and no tables
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