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.

25 pages, 2 figures, 1 table. Matches version published in Physics of the Dark Universe

References in corpus (18)

• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• The 1% Concordance Hubble Constant
• Lorentz-violation-induced arrival delays of cosmological particles
• Search for Lorentz Invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944
• Absence of Black Holes at LHC due to Gravity's Rainbow
• Tests of Lorentz symmetry in the gravitational sector
• Rainbow universe
• A Proposal for Testing Gravity's Rainbow
• Gravitational Collapse in Gravity's Rainbow
• Exact solutions and phenomenological constraints from massive scalars in a Gravity's Rainbow spacetime
• Constraints on rainbow gravity functions from black hole thermodynamics
• The kinematics of particles moving in rainbow spacetime
• Varying constants quantum cosmology
• Quantum Gravity Effects On Charged Micro Black Holes Thermodynamics
• Note on the speed of GW150914 in gravity's rainbow
• The Standard-Model Extension and Gravitational Tests

Cited by in corpus (9)

• GUP Modified Hawking Radiation in Bumblebee Gravity
• Redshift and lateshift from homogeneous and isotropic modified dispersion relations
• Thermal analysis of photon-like particles in rainbow gravity
• Aharonov-Bohm effect for bound states in the cosmic string spacetime in the context of rainbow gravity
• $Ad{S}_4$ dyonic black holes in gravity's rainbow
• Hořava-Lifshitz cosmology in light of new data
• A Special Lorentz Violation Model and a Special Rainbow Function
• Correction to the quantum relation of photons in the Doppler effect based on a special Lorentz violation model
• Einstein-Yang-Mills Regular Black Holes in Rainbow Gravity