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High-order primordial perturbations with quantum gravitational effects

Tao Zhu1,2,*, Anzhong Wang1,2,3,†, Klaus Kirsten4,‡, Gerald Cleaver5,§, and Qin Sheng4,¶

  • 1Institute for Advanced Physics & Mathematics, Zhejiang University of Technology, Hangzhou 310032, China
  • 2GCAP-CASPER, Physics Department, Baylor University, Waco, Texas 76798-7316, USA
  • 3Departamento de Física Teórica, Instituto de Física, UERJ, 20550-900 Rio de Janeiro, Brazil
  • 4GCAP-CASPER, Mathematics Department, Baylor University, Waco, Texas 76798-7328, USA
  • 5EUCOS-CASPER, Physics Department, Baylor University, Waco, Texas 76798-7316, USA

  • *Tao_Zhu@baylor.edu
  • †anzhong_wang@baylor.edu
  • ‡klaus_kirsten@baylor.edu
  • §gerald_cleaver@baylor.edu
  • qin_sheng@baylor.edu
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Phys. Rev. D 93, 123525 – Published 29 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.123525

Abstract

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.

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References (27)

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Phys. Rev. D 93, 123525– Published 29 June, 2016
  • Received 2 May 2016

© 2016 American Physical Society

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