Gravity's rainbow: a bridge between LQC and DSR

Abstract

The doubly special relativity (DSR) theories are investigated in order to take into account an observer-independent length scale in special relativity framework. It is widely believed that any quantum theory of gravity would reduce to a DSR model at the flat limit when purely gravitational and quantum mechanical effects are negligible. Gravity's rainbow is a simple generalization of DSR theories to incorporate gravity. In this paper, we show that the effective Friedmann equations that are suggested by loop quantum cosmology (LQC) can be exactly reobtained in rainbow cosmology setup. The deformed geometry of LQC then completely fixes the modified dispersion relation and results in unique DSR model. In comparison with standard LQC scenario where only the geometry is modified, both of the geometry and matter parts get modifications in our setup. In this respect, we find that the total number of microstates for the universe is finite which suggests the statistical origin for the energy and entropy density bounds. These results explicitly show that the DSR theories are appropriate candidates for the flat limit of loop quantum gravity.

10 pages, 4 figures, Refs. added

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• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Quantum corrections to the thermodynamics and phase transition of a black hole surrounded by a cavity in the extended phase space
• The extended phase space thermodynamics of Planck-scale-corrected Reissner-Nordström-anti-de Sitter black hole
• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
• 5-Dimensional $SO(1,4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal
• Observational Constraints on Asymptotic Safety Inflation in Gravity Rainbow
• Gravitational baryogenesis in $F(R)$ gravity's rainbow
• Thermodynamic analysis of a compact object in Rastall-Rainbow gravity
• The effect of loop quantum gravitational rainbow functions on the formation of naked singularities