Conformal transformation route to gravity's rainbow

TL;DR

This paper employs conformal transformations to analyze gravity's rainbow, revealing energy-dependent modifications to gravitational constants and connecting it to energy-dependent $f(R)$ gravity theories.

Contribution

It introduces a conformal transformation approach to derive energy-dependent gravitational modifications in gravity's rainbow and links it to $f(R)$ gravity frameworks.

Findings

Derived a specific form of modified Newton's and cosmological constants in gravity's rainbow.

Showed that gravity's rainbow can be described by an energy-dependent $f(E,\tilde R)$ gravity.

Demonstrated that $f(R)$ gravity can be extended to an energy-dependent $ ilde f(E,\tilde R)$ form.

Abstract

Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we would consider the gravity's rainbow, in which the metric could be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of 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 the Einstein gravity's rainbow could be described by an energy-dependent $f(E,\tilde R)$ gravity. At last, we study the $f(R)$ gravity, when the gravity's rainbow is considered, it can also be described as another energy-dependent $\tilde f(E,\tilde R)$ gravity.