A Proposal for Testing Gravity's Rainbow

TL;DR

This paper explores how gravity's rainbow, a theory modifying general relativity with quantum gravity insights, affects classical tests of gravity, providing bounds on the theory's parameters through experimental comparisons.

Contribution

It investigates the Schwarzschild metric within gravity's rainbow using three known modified dispersion relations, analyzing their effects on key gravitational phenomena.

Findings

Bounds on rainbow function parameters derived from experiments

Effects on light deflection and gravitational red-shift quantified

Consistency checks with classical tests of gravity

Abstract

Various approaches to quantum gravity such as string theory, loop quantum gravity and Horava-Lifshitz gravity predict modifications of the energy-momentum dispersion relation. Magueijo and Smolin incorporated the modified dispersion relation (MDR) with the general theory of relativity to yield a theory of gravity's rainbow. In this paper, we investigate the Schwarzschild metric in the context of gravity's rainbow. We investigate rainbow functions from three known modified dispersion relations that were introduced by Amelino-Camelia, et el. in [arXiv:hep-th/9605211, arXiv:0806.0339v2, arXiv:astro-ph/9712103] and by Magueijo-Smolin in [arXiv:hep-th/0112090]. We study the effect of the rainbow functions on the deflection of light, photon time delay, gravitational red-shift, and the weak equivalence principle. We compare our results with experiments to obtain upper bounds on the parameters of the rainbow functions.