Conformal transformation route to gravity’s rainbow

  • Miao He
  • Ping Li
  • Zi-Liang Wang
  • Jia-Cheng Ding
  • Jian-Bo Deng
Research Article


Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we consider gravity’s rainbow, in which the metric can be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of a modified Newton’s constant and cosmological constant in gravity’s rainbow, which implies that the total vacuum energy is dependent on probe energy. Moreover, the result shows that Einstein gravity’s rainbow can be described by energy-dependent \(f(E,\tilde{R})\) gravity. At last, we study the f(R) gravity, when gravity’s rainbow is considered, which can also be described as energy-dependent \(\tilde{f}(E,\tilde{R})\) gravity.


Conformal transformation Gravity’s rainbow f(R) Gravity 



We would like to thank the National Natural Science Foundation of China (Grant No. 11571342) for supporting us on this work.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Miao He
    • 1
  • Ping Li
    • 1
  • Zi-Liang Wang
    • 1
  • Jia-Cheng Ding
    • 1
  • Jian-Bo Deng
    • 1
  1. 1.Institute of Theoretical PhysicsLanZhou UniversityLanzhouPeople’s Republic of China

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