Gravity's rainbow: a bridge between LQC and DSR

TL;DR

This paper demonstrates that loop quantum cosmology's effective Friedmann equations can be exactly derived within a gravity's rainbow framework, establishing a link between DSR theories and quantum gravity effects.

Contribution

It shows that rainbow cosmology can reproduce LQC equations and uniquely determine the DSR model, connecting quantum gravity with modified dispersion relations.

Findings

Effective Friedmann equations are exactly recovered in rainbow cosmology.

The geometry and matter modifications lead to finite universe microstates.

Results support DSR as the flat limit of loop quantum gravity.

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.