Energy Scale of Lorentz Violation in Rainbow Gravity

TL;DR

This paper explores Lorentz violation at high energies within Rainbow Gravity, modifies cosmological equations accordingly, and constrains the violation scale to near the GUT energy level using observational data.

Contribution

It introduces energy-dependent functions into Rainbow Gravity, derives modified cosmological equations, and constrains the Lorentz violation scale using cosmological observations.

Findings

Lorentz violation scale constrained to ≥10^{16} GeV

Modified cosmological equations derived from Rainbow Gravity

Energy dependence of gravitational and cosmological constants modeled

Abstract

We modify the standard relativistic dispersion relation in a way which breaks Lorentz symmetry - the effect is predicted in a high-energy regime of some modern theories of quantum gravity. We show that it is possible to realise this scenario within the framework of Rainbow Gravity which introduces two new energy-dependent functions $f_1(E)$ and $f_2(E)$ into the dispersion relation. Additionally, we assume that the gravitational constant $G$ and the cosmological constant $\Lambda$ also depend on energy $E$ and introduce the scaling function $h(E)$ in order to express this dependence. For cosmological applications we specify the functions $f_1$ and $f_2$ in order to fit massless particles which allows us to derive modified cosmological equations. Finally, by using Hubble+SNIa+BAO(BOSS+Lyman $\alpha$)+CMB data, we constrain the energy scale $E_{LV}$ to be at least of the order of $10^{16}$ GeV at $1\sigma$ which is the GUT scale or even higher $10^{17}$ GeV at $3\sigma$. Our claim is that this energy can be interpreted as the decoupling scale of massless particles from spacetime Lorentz violating effects.