Title: Energy Scale of Lorentz Violation in Rainbow Gravity,
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.