The Varying Speed of Light in Eddington-inspired Born-Infield Gravity with Rainbow Metric

TL;DR

This paper explores a varying speed of light theory within Eddington-inspired Born-Infeld gravity, incorporating rainbow metrics that depend on test particle energy, and analyzes how universe energy density affects light speed.

Contribution

It introduces a novel bi-metric gravity framework with energy-dependent rainbow metrics in EiBI gravity and examines the impact on the speed of light in cosmological models.

Findings

Test particle energy increases with universe energy density.

Sign of parameter κ influences the trend of light speed variation.

Different rainbow functions yield distinct behaviors of light speed.

Abstract

In this paper, we proposed that at each point of spacetime, in addition to the Riemannian metric tensor which describes the geometry of spacetime and the gravitational field, there is an rainbow metric tensor which shows the geometry of spacetime depends on the energy of the test particle. Because Eddington-inspired Born-Infield(EiBI) gravity can be seen as a special bi-metric gravity, we research a varying speed of light theory for a bi-metric gravity corresponding to EiBI gravity. For FRW universe, we find the energy of test particle will increase with rising energy density of universe. We also research the varying speed of light for three different kinds of rainbow functions and find the sign of parameter $\kappa$ would influence the trend of spend of light.