Gravity's Rainbow: a bridge towards Horava-Lifshitz gravity

TL;DR

This paper explores the theoretical link between Gravity's Rainbow and Horava-Lifshitz gravity, focusing on their UV modifications and implications for quantum gravity, by deriving and comparing their Wheeler-DeWitt equations in symmetric geometries.

Contribution

It establishes a novel correspondence between Gravity's Rainbow and Horava-Lifshitz gravity through their Wheeler-DeWitt equations in symmetric spacetimes.

Findings

Derived Wheeler-DeWitt equations for both theories.

Established a formal bridge connecting the two frameworks.

Highlighted implications for quantum gravity research.

Abstract

We investigate the connection between Gravity's Rainbow and Horava-Lifshitz gravity, since both theories incorporate a modification in the UltraViolet regime which improves their quantum behavior at the cost of the Lorentz invariance loss. In particular, extracting the Wheeler-De Witt equations of the two theories in the case of Friedmann-Lemaitre-Robertson-Walker and spherically symmetric geometries, we establish a correspondence that bridges them.